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Physics has recently opened up vast new fields 
knowledge making it necessary for us to modify some of 
our most basic philosophical and scientific concepts — 
the pillars of cultures and civilizations. This, says F. S. C. 
Northrop in his introduction to the present volume, is 
'the major event of today's and tomorrow's worfd'. 

Werner Heisenberg was born in Wijrzburg, Germany, 
in 1901. He was educated at the universities of Munich 
and Gottingen and in 1932 was awarded the Nobel 
Prize for his work in theoretical atomic physics. He is 
now Director of the Max Planck Institute for Physics 
and Astrophysics in Munich. Author of many books, 
his memories of a life in science have recently appeared 
under the title Physics and Beyond: Encounters and 
Conversations (World Perspectives No. 23). 

'Here we are moving away the great peaks of intellectual 
endeavour, where the boundaries of the subject are 
transcended and all knowledge is seen to be one : it is 
a master hand that is leading us.' 

Books of the Month 

. the reader must realize that in this series of stimulat- 
ing lectures, Heisenberg is making him think. Anyone 
who is willing to do so will find the book most re- 

Institute of Physics and the Physical Society 

ISBN 04 530016 X 


unwin university books 

I ^ferner Heisenben 

ysics an 

the revolution i 
modern scieno 


unwin university hooks 


Planned and edited by Ruth Nanda Anshen 


Kenneth Clark, Richard Courant 

Werner Heisenberg, Ivan Mich 

Konrad Lorenz, Joseph Needham 

I. I. Rabi, Sarvepalli Radhakrishnan 

Karl Rahner, Alexander Sachs 

C. N. Yang 

Approaches to God, Jacques Maritain 

Recovery of Faith, Sarvepalli Radhakrishnan 

The Art of Loving, Erich Fromm 

Physics and Beyond, Werner Heisenberg 

Sigmund Freud's Mission, Erich Fromm 

Mirage of Health, Rene' Dubos 

Voices of Man, Mario Pei 

Myth and Reality, Mircea Eliade 

The Meaning of the Twentieth Century, Kenneth E. Boulding 



Physics and 


Ruskin House 


First published in Great Britain in 1 959 
Second impression 1963 
Third impression 19J1 

This book is copyright under the Berne Convention. All rights are reserved. 
Apart from any fair dealing for the purpose of private study, research, 
criticism or review, as permitted under the Copyright Act, J 956, no part 
of this publication may be reproduced, stored in a retrieval system, or 
transmitted, in any form or by any means, electronic, electrical, chemical, 
mechanical, optical, photocopying recording or otherwise, without the 
prior permission of the copyright owner. Enquiries should be addressed to 
the publishers. 

© Werner Heisenberg, 1958 
isbn o 04 J30016 x \yr 

' jimu-",.u;.« M.MMh.m . 

<^60847 , 

Printed in Great Britain 


John Dickens &. Co Ltd 




world perspectives is a plan to present short books in a variety 
of fields by the most responsible of contemporary thinkers. The 
purpose is to reveal basic new trends in modern civilization, to 
interpret the creative forces at work in the East as well as in the 
West, and to point to the new consciousness which can contri- 
bute to a deeper understanding of the inter-relation of man and 
the universe, the individual and society, and of the values shared 
by all people, world perspectives represents the world com- 
munity of ideas in a universe of discourse, emphasising the prin- 
ciple of unity in mankind, of permanence within change. 

Recent developments in many fields of thought have opened 
unsuspected prospects for a deeper understanding of man's situa- 
tion and for a proper appreciation of human values and human 
aspirations. These prospects, though the outcome of purely 
specialized studies in limited fields, require for their analysis and 
synthesis a new structure and frame in which they can be ex- 
plored, enriched and advanced in all their aspects for the benefit 
of man and society. Such a structure and frame it is the endeavour 
of world perspectives to define leading hopefully to a doctrine 
of man. 

A further purpose of this Series is to attempt to overcome a 
principal ailment of humanity, namely, the effects of the atomi- 
zation of knowledge produced by the overwhelming accretion of 
facts which science has created; to clarify and synthesise ideas 
through the depth fertilization of minds; to show from diverse 
and important points of view the correlation of ideas, facts and 
values which are in perpetual interplay; to demonstrate the 
character, kinship, logic and operation of the entire organism of 
reality while showing the persistent inter-relationship of the 
processes of the human mind and in the interstices of knowledge, 
to reveal the inner synthesis and organic unity of life itself. 

It is the thesis of world perspectives that in spite of the 




difference and diversity of the disciplines represented, there 
exists a strong common agreement among its authors concerning 
the overwhelming need for counterbalancing the multitude of 
compelling scientific activities and investigations of objective 
phenomena from physics to metaphysics, history and biology 
and to relate these to meaningful experience. To provide this 
balance, it is necessary to stimulate an awareness of the basic 
fact that ultimately the individual human personality must tie 
all the loose ends together into an organic whole, must relate 
himself to himself, to mankind and society while deepening and 
enhancing his communion with the universe. To anchor this 
spirit and to impress it on the intellectual and spiritual life of 
humanity, on thinkers and doers alike, is indeed an enormous 
challenge and cannot be left entirely either to natural science 
on the one hand or to organized religion on the other. For we 
are confronted with the unbending necessity to discover a 
principle of differentiation yet relatedness lucid enough to justify 
and purify scientific, philosophic and all other knowledge while 
accepting their mutual interdependence. This is the crisis in 
consciousness made articulate through the crisis in science. This 
is the new awakening. 

This Series is committed to the recognition that all great 
changes are preceded by a vigorous intellectual re-evaluation and 
reorganization. Our authors are aware that the sin of hubris may 
be avoided by showing that the creative process itself is not a free 
activity if by free we mean arbitrary or unrelated to cosmic law. 
For the creative process in the human mind, the development 
process in organic nature and the basic laws of the inorganic 
realm may be but varied expressions of a universal formative 
process. Thus world perspectives hopes to show that although 
the present apocalytic period is one of exceptional tensions, there 
is also an exceptional movement at work towards a compen- 
sating unity which cannot violate the ultimate moral power 
pervading the universe, that very power on which all human 
effort must at last depend. In this way, we may come to under- 
stand that there exists an independence of spiritual and mental 
growth which though conditioned by circumstances is never 
determined by circumstances. In this way the great plethora of 
human knowledge may be correlated with an insight into the 


nature of human nature by being attuned to the wide and deep 
range of human thought and human experience. For what is 
lacking is not the knowledge of the structure of the universe but 
a consciousness of the qualitative uniqueness of human life. 

And finally, it is the thesis of this Series that man is in the 
process of developing a new awareness which, in spite of his 
apparent spiritual and moral captivity, can eventually lift the 
human race above and beyond the fear, ignorance, brutality and 
isolation which beset it to-day. It is to this nascent consciousness, 
to this concept of man born out of a fresh vision of reality, that 
world perspectives is dedicated. 





What This Series Means 


i An Old and a New Tradition 32 

2 The History of Quantum Theory 34 

3 The Copenhagen Interpretation of Quantum 

Theory 46 

4 Quantum Theory and the Roots of Atomic 

Science 58 

5 The Development of Philosophical Ideas Since 

Descartes in Comparison with the New 
Situation in Quantum Theory 71 

6 The Relation of Quantum Theory to Other 

Parts of Natural Science 85 

7 The Theory of Relativity 99 

8 Criticism and Counter-proposals to the Copen- 

hagen Interpretation of Quantum Theory 114 

9 Quantum Theory and the Structure of Matter 129 

10 Language and Reality in Modern Physics 145 

11 The Role of Modern Physics- in the Present 

Development of Human Thinking 161 


by F. S. C. Northrop 

Sterling frolessor ol Thilosophy and Law, 
The Law School, Yale University 

THERE is a general awareness that contemporary physics has 
brought about an important revision in man's conception of the 
universe and his relation to it. The suggestion has been made 
that this revision pierces to the basis of man's fate and freedom, 
affecting even his conception of his capacity to control his own 
destiny. In no portion of physics does this suggestion show itself 
more pointedly than in the principle of indeterminacy of quan- 
tum mechanics. The author of this book is the discoverer of this 
principle. In fact, it usually bears his name. Hence, no one is more 
competent to pass judgment on what it means than he. 

In his previous book. The Physical Principles oi the Quantum 
Theory,* Heisenberg gave an exposition of the theoretical 
interpretation, experimental meaning and mathematical appa- 
ratus of quantum mechanics for professional physicists. Here 
he pursues this and other physical theories with respect to their 
philosophical implications and some of their likely social conse- 
quences for the layman. More specifically, he attempts here to 
raise and suggest answers to three questions: (i) What do the 
experimentally verified theories of contemporary physics affirm? 
(2) How do they permit or require man to think of himself in 
relation to his universe? (3) How is this new way of thinking, 
which is the creation of the modern West, going to affect other 
parts of the world? 

The third of these questions is dealt with briefly by Heisenberg 
at the beginning and end of this inquiry. The brevity of his 
remarks should not lead the reader to pass lightly over their im- 
port. As he notes, whether we like it or not, modern ways are 
going to alter and in part destroy traditional customs and values. 

* University of Chicago Press, Chicago, 1930. 



It is frequently assumed by native leaders of non-Western 
societies, and also often by their Western advisers, that the prob- 
lem of introducing modern scientific instruments and ways into 
Asia, the Middle East and Africa is merely that of giving the 
native people their political independence and then providing 
them with the funds and the practical instruments. This facile 
assumption overlooks several things. First, the instruments of 
modern science derive from its theory and require a comprehen- 
sion of that theory for their correct manufacture or effective 
use. Second, this theory in turn rests on philosophical, as well as 
physical, assumptions. When comprehended, these philosophical 
assumptions generate a personal and social mentality and 
behaviour quite different from, and at points incompatible with, 
the family, caste and tribally centred mentality and values of 
the native Asian, Middle Eastern or African people. In short, one 
cannot bring in the instruments of modern physics without 
sooner or later introducing its philosophical mentality, and this 
mentality, as it captures the scientifically trained youth, up- 
sets the old familial and tribal moral loyalties. If unnecessary 
emotional conflict and social demoralization are not to result, 
it is important that the youth understand what is happening to 
them. This means that they must see their experience as the 
coming together of two different philosophical mentalities, that 
of their traditional culture and that of the new physics. Hence, 
the importance for everyone of understanding the philosophy of 
the new physics. 

But it may be asked, Isn't physics quite independent of 
philosophy? Hasn't modern physics become effective only by 
dropping philosophy? Clearly, Heisenberg answers both of these 
questions in the negative. Why is this the case? 

Newton left the impression that there were no assumptions in 
his physics which were not necessitated by the experimental 
data. This occurred when he suggested that he made no hypoth- 
eses and that he had deduced his basic concepts and laws from 
the experimental findings. Were this conception of the relation 
between the physicist's experimental observations and his theory 
correct, Newton's theory would never have required modifica- 
tion, nor could it ever have implied consequences which experi- 
ment does not confirm. Being implied by the facts, it would be 



as indubitable and final as they are. 

In 1885, however, an experiment performed by Michelson 
and Morley revealed a fact which should not exist were the 
theoretical assumptions of Newton the whole truth. This made 
it evident that the relation between the physicist's experimenal 
facts and his theoretical assumptions is quite other than what 
Newton had led many modern physicists to suppose. When, 
some ten years later, experiments on radiation from black bodies 
enforced an additional reconstruction in Newton's way of think- 
ing about his subject matter, this conclusion became inescapable. 
Expressed positively, this means that the theory of physics is 
neither a mere description of experimental facts nor something 
deducible from such a description; instead, as Einstein has 
emphasized, the physical scientist only arrives at his theory by 
speculative means. The deduction in his method runs not from 
facts to the assumptions of the theory but from the assumed 
theory to the facts and the experimental data. Consequently, 
theories have to be proposed speculatively and pursued deduc- 
tively with respect to their many consequences so that they can 
be put to indirect experimental tests. In short, any theory of 
physics makes more physical and philosophical assumptions than 
the facts alone give or imply. For this reason, any theory is sub- 
ject to further modification and reconstruction with the advent 
of new evidence that is incompatible, after the manner of the 
results 1 of the Michelson-Morley experiment, with its basic as- 

These assumptions, moreover, are philosophical in character. 
They may be ontological, i.e., referring to the subject matter of 
scientific knowledge which is independent of its relation to the 
perceiver; or they may be epistemological, i.e., referring to the 
relation of the scientist as experimenter and knower to the 
subject matter which he knows. Einstein's special and general 
theories of relativity modify the philosophy of modern physics 
in the first of these two respects by radically altering the 
philosophical theory of space and time and their relation to 
matter. Quantum mechanics, especially its Heisenberg principle 
of indeterminacy, has been notable for the change it has brought 
in the physicist's epistemological theory of the relation of the 
experimenter to the object of his scientific knowledge. Perhaps 



the most novel and important thesis of this book is its author's 
contention that quantum mechanics has brought the concept of 
potentiality back into physical science. This makes quantum 
theory as important for ontology as for epistemology. At this 
point, Heisenberg's philosophy of physics has an element in 
common with that of Whitehead. 

It is because of this introduction of potentiality into the subject 
matter of physics, as distinct from the epistemological predica- 
ment of physicists, that Einstein objected to quantum mechanics. 
He expressed this objection by saying: 'God does not play dice.' 
The point of this statement is that the game of dice rests on the 
laws of chance, and Einstein believed that the latter concept finds 
its scientific meaning solely in the epistemological limitations of 
the finite knowing mind in its relation to the omnicomplete 
object of scientific knowledge and, hence, is misapplied when 
referred ontologically to that object itself. The object being per 
se all complete and in this sense omniscient, after the manner of 
God, the concept of chance or of probability is inappropriate for 
any scientific description of it. 

This book is important because it contains Heisenberg's answer 
to this criticism of his principle of indeterminacy and of quantum 
theory by Einstein and by others. In understanding this answer 
two things must be kept in mind: (i) The aforementioned rela- 
tion between the data of experimental physics and the concepts 
of its theory. (2) The difference between the role of the concept 
of probability in (a) Newton's mechanics and Einstein's theory 
of relativity and in (b) quantum mechanics. Upon (i), Einstein 
and Heisenberg, and relativistic mechanics and quantum 
mechanics, are in agreement. It is only with respect to (2) that 
they differ. Yet the reason for Heisenberg's and the quantum 
physicist's difference from Einstein on (2) depends in consider- 
able part on (i) which Einstein admits. 

( i) affirms that the experimental data of physics do not imply 
its theoretical concepts. From this it follows that the object of 
scientific knowledge is never known directly by observation or 
experimentation, but is only known by speculatively proposed 
theoretic construction or axiomatic postulation, tested only 
indirectly and experimentally via its deduced consequences. To 
find the object of scientific knowledge we must go, therefore, 



to its theoretical assumptions. 

When we do this for (a) Newton's or Einstein's mechanics 
and for (b) quantum mechanics, we discover that the concept 
of probability or chance enters into the definition of the state of 
a physical system, and, in this sense, into its subject matter, in 
quantum mechanics, but does not do so in Newton's mechanics 
or Einstein's theory of relativity. This undoubtedly is what 
Heisenberg means when he writes in this book that quantum 
theory has brought the concept of potentiality back into physical 
science. It is also, without question, what Einstein has in mind 
when he objects to quantum theory. 

Put more concretely, this difference between quantum 
mechanics and the previous physical theories may be expressed 
as follows: In Newton's and Einstein's theory, the state of any 
isolated mechanical system at a given moment of time is given 
precisely when only numbers specifying the position and 
momentum of each mass in the system are empirically deter- 
mined at that moment of time; no numbers referring to a proba- 
bility are present. In quantum mechanics the interpretation of 
an observation of a system is a rather complicated procedure. The 
observation may consist in a single reading, the accuracy of 
which has to be discussed, or it may comprise a complicated set 
of data, such as the photograph of the water droplets in a cloud 
chamber; in any case, the result can be stated only in terms of a 
probability distribution concerning, for instance, the position or 
momentum of the particles of the system. The theory then pre- 
dicts the probability distribution for a future time. The theory is 
not experimentally verified when that future state arrives if 
merely the momentum or position numbers in a particular ob- 
servation lie within the predicted range. The same experiment 
with the same initial conditions must be repeated many times, 
and the values of position or momentum, which may be different 
in each observation, must similarly be found to be distributed ac- 
cording to the predicted probability distribution. In short, the 
crucial difference between quantum mechanics and Einstein's or 
Newton's mechanics centres in the definition of a mechanical 
system at any moment of time, and this difference is that quan- 
tum mechanics introduces the concept of probability into its 
definition of state and the mechanics of Newton and Einstein 



does not. 

This does not mean that probability had no place in Newton's 
or Einstein's mechanics. Its place was, however, solely in the 
theory of errors by means of which the accuracy of the Yes or 
No verification or nonconfirmation of the prediction of the 
theory was determined. Hence, the concept of probability and 
chance was restricted to the epistemological relation of the 
scientist in the verification of what he knows; it did not enter 
into the theoretical statement of what he knows. Thus, Einstein's 
dictum that 'God does not play dice' was satisfied in his two 
theories of relativity and in Newton's mechanics. 

Is there any way of deciding between Einstein's contention 
and that of Heisenberg and other quantum theorists? Many 
answers have been given to this question. Some physicists and 
philosophers, emphasizing operational definitions, have argued 
that, since all physical theories, even classical ones, entail human 
error and uncertainties, there is nothing to be decided between 
Einstein and the quantum theorists. This, however, is (a) to 
overlook the presence of axiomatically constructed, constitutive 
theoretic definitions as well as theory-of-errors, operational 
definitions in scientific method and (b) to suppose that the 
concept of probability and the even more complex uncertainty 
relation enter into quantum mechanics only in the operational- 
definition sense. Heisenberg shows that the latter supposition 
is false. 

Other scientists and philosophers, going to the opposite ex- 
treme, have argued that, merely because there is uncertainty in 
predicting certain phenomena, this constitutes no argument 
whatever for the thesis that these phenomena are not completely 
determined. This argument combines the statical problem of 
defining the state of a mechanical system at a given time with 
the dynamical or casual problem of predicting changes in the 
state of the system through time. But the concept of probability 
in quantum theory enters only into its statics, i.e., its theoretical 
definition of state. The reader will find it wise, therefore, to keep 
distinct these two components, i.e., the statical theoretical 
definition-of -state component and the dynamic, or casual, theo- 
retical change-of -state-through-time component. With respect to 
the former, the concept of probability and the attendant un- 



certainty enter theoretically and in principle; they do not refer 
merely to the operational and epistemological uncertainties and 
errors, arising from the finitness of, and inaccuracies in, human 
behaviour, that are common to any scientific theory and any 
experimentation whatsoever. 

But, why, it may be asked, should the concept of probability 
be introduced into the theoretic definition of the state of a me- 
chanical system at any statical moment t 1 in principle? In making 
such a theoretical construct by axiomatic postulation, do not 
Heisenberg and quantum theoreticians generally beg the ques- 
tion at issue between themselves and Einstein? This book makes 
it clear that the answer to these questions is as follows: The 
reason for the procedure of quantum mechanics is thesis (1) 
above, which Einstein himself also accepts. 

Thesis (1) is that we know the object of scientific knowledge 
only by the speculative means of axiomatic theoretic construc- 
tion or postulation; Newton's suggestion that the physicist can 
deduce our theoretical concepts from the experimental data 
being false. It follows that there is no a priori or empirical mean- 
ing for affirming that the object of scientific knowledge, or, more 
specifically, the state of a mechanical system at a given time t 1 , 
must be defined in a particular way. The sole criterion is, which 
set of theoretic assumptions concerning the subject matter of 
mechanics when pursued to their deduced experimental conse- 
quences is confirmed by the experimental data? 

Now, it happens that when we theoretically and in principle 
define the state of a mechanical system for subatomic phe- 
nomena in terms solely of numbers referring to position and 
momentum, as Einstein would have us do, and deduce the 
consequences for radiation from black bodies, this theoretical 
assumption concerning the state of a mechanical system and the 
subject matter of atomic physics is shown to be false by experi- 
mental evidence. The experimental facts simply are not what the 
theory calls for. When, however, the traditional theory is modi- 
fied with the introduction of Planck's constant and the addition 
in principle of the second set of numbers referring to the proba- 
bility that the attached position-momentum numbers will be 
found, from which the uncertainty principle follows, the experi- 
mental data confirm the new theoretical concepts and principles. 



In short, the situation in quantum mechanics with respect to 
experiments on black-body radiation is identical with that faced 
by Einstein with respect to the Michelson-Morley experiment. In 
both cases, only by introducing the new theoretical assumption 
in principle is physical theory brought into accord with the ex- 
perimental facts. Thus, to assert that, notwithstanding quantum s 
mechanics, the positions and momenta of subatomic masses are 
'really' sharply located in space and time as designated by one 
pair of numbers only, and, hence, completely deterministic caus- 
ally, as Einstein and the aforementioned philosophers of science 
would have one do, is to affirm a theory concerning the subject 
matter of physical knowledge which experiments on black-body 
radiation have shown to be false in the sense that a deductive 
experimental consequence of this theory is not confirmed. 

It does not follow, of course, that some new theory compatible 
with the foregoing experimental facts might not be discovered in 
which the concept of probability does not enter in principle into 
its definition of state. Professor Norbert Wiener, for example, 
believes that he has clues to the direction such a theory might 
take. It would, however, have to reject a definition of state in 
terms of the four space-time dimensions of Einstein's theory and 
would, therefore, be incompatible with Einstein's thesis on other 
grounds. Certainly, one cannot rule out such a possibility. 
Nevertheless, until such an alternative theory is presented, any- 
one, who does not claim to possess some a priori or private 
source of information concerning what the object of scientific 
knowledge must be, has no alternative but to accept the defini- 
tion of state of quantum theory and to affirm with the author of 
this book that it restores the concept of potentiality to the object 
of modern scientific knowledge. Experiments on black-body 
radiation require one to conclude that God plays dice. 

What of the status of causality and determinism in quantum 
mechanics? Probably the interest of the layman and the humanist 
in this book depends most on its answer to this question. 

If this answer is to be understood, the reader must pay par- 
ticular attention to Heisenberg's description of (a) the afore- 
mentioned definition of state by recourse to the concept of 
probability and (b) the Schrodinger time-equation. The reader 
must also make sure, and this is the most difficult task of all, that 



the meaning of the words 'causality' and 'determinism' in his 
mind when he asks the above question is identical with the 
meaning these words have in Heisenberg's mind when he speci- 
fies the answer. Otherwise, Heisenberg will be answering a 
different question from the one the reader is asking and com- 
plete misunderstanding upon the reader's part will occur. 

The situation is further complicated by the fact that modern 
physics permits the concept of causality to have two different 
scientifically precise meanings, the one stronger than the other, 
and there is no agreement among physicists about which one of 
these two meanings the word 'causality' is to be used to desig- 
nate. Hence, some physicists and philosophers of science use the 
word to designate the stronger of the two meanings. There is 
evidence, at times at least, that this is Professor Heisenberg's 
usage in this book. Other physicists and philosophers, including 
the writer of this Introduction, use the word 'causality' to 
designate the weaker of the two meanings and the word 'de- 
terminism' to designate the stronger meaning. When the former 
usage is followed, the words 'causality' and 'determinism' 
become synonymous. When the second usage is followed, every 
deterministic system is a causal system, but not every causal 
system is deterministic. 

Great confusion has entered into previous discussion of this 
topic because frequently neither the person who asks the ques- 
tion nor the physicist who has answered it has been careful to 
specify in either question or answer whether he is using the word 
'causality' in its weaker or in its stronger modern scientific 
meaning. If one asks 'Does causality hold in quantum me- 
chanics?' not specifying whether one is asking about causality 
in its stronger or in its weaker sense, one then gets apparently 
contradictory answers from equally competent physicists. One 
physicist, taking the word 'causality' in its stronger sense, quite 
correctly answers 'No'. The other physicist, taking 'causality' 
in its weaker sense, equally correctly answers 'Yes'. Naturally 
the impression has arisen that quantum mechanics is not specific 
about what the answer is. Nevertheless, this impression is 
erroneous. The answer of quantum mechanics becomes unequiv- 
ocal the moment one makes the question and the answer 
unambiguous by specifying which meaning of 'causality' one is 



talking about. 

It is important, therefore, to become clear about different 
possible meanings of the word 'causality'. Let us begin with the 
layman's common-sense usage of the word 'cause' and then move 
to the more exact meanings in modern physics, considering the 
meaning in Aristotle's physics on the way. n 

One may say 'The stone hit the window and caused the glass 
to break.' In this use of 'causality' it is thought of as a relation 
between objects, i.e., between the stone and the windowpane. 
The scientist expresses the same thing in a different way. He 
describes the foregoing set of events in terms of the state of the 
stone and the windowpane at the earlier time t 1 when the stone 
and the windowpane were separated and the state of this same 
system of two objects at the later time t 2 when the stone and the 
windowpane collided. Consequently, whereas the layman tends 
to think of causality as a relation between objects, the scientist 
thinks of it as a relation between different states of the same 
object or the same system of objects at different times. 

This is why, in order to determine what quantum mechanics 
says about causality, one must pay attention to two things: (i) 
The state-function which defines the state of any physical system 
at any specific time t. (2) The Schrodinger time-equation which 
relates the state of the physical system at the earlier time t 1 to its 
different state at any specifiable later time t 2 . What Heisenberg 
says about (1) and (2) must, therefore, be read with meticulous 

It will help to understand what quantum mechanics says 
about the relation between the states of a given physical object, 
or system of physical objects', at different times if we consider the 
possible properties that this relation might have. The weakest 
possible case would be that of mere temporal succession with no 
necessary connection whatever and with not even a probability, 
however small, that the specifiable initial state will be followed 
in time by a specifiable future state. Hume give us reasons for 
believing that the relation between the sensed states of im- 
mediately sensed natural phenomena is of this character. Cer- 
tainly, as he pointed out, one does not sense any relation of 
necessary connection. Nor does one directly sense probability. 
All that sensation gives us with respect to the successive states of 



any phenomenon is the mere relation of temporal succession. 

This point is of great importance. It means that one can arrive 
at a causal theory in any science or in common-sense knowledge, 
or even at a probability theory, of the relation between the suc- 
cessive states of any object or system, only by speculative means 
and axiomatically constructed, deductively formulated scientific 
and philosophical theory which is tested not directly against the 
sensed and experimental data but only indirectly by way of its 
deductive consequences. 

A second possibility with respect to the character of the rela- 
tion between the states of any physical system at different times 
is that the relation is a necessary one, but that one can know 
what this necessary connection is only by knowing the future 
state. The latter knowledge of the future state may be obtained 
either by waiting until it arrives or by having seen the future or 
final state of similar systems in the past. When such is the case, 
causality is teleological. Changes of the system with time are 
determined by the final state or goal of the system. The physical 
system which is an acorn in the earlier state t 1 and an oak tree 
in the later state t 2 is an example. The connection between these 
two states seems to-be a necessary one. Acorns never change into 
maple trees or into elephants. They change only into oaks. Yet, 
given the properties of this physical system in the acorn state of 
the earlier time t\ no scientist has as yet been able to deduce 
the properties of the oak tree which the system will have at the 
later time t 2 . Aristotelian physics affirmed that all causal rela- 
tions are teleological. 

Another possibility is that the relation between the states of 
any object, or any system of objects, at different times is a 
relation of necessary connection such that, given knowledge of 
the initial state of the system, assuming isolation, its future state 
can be deduced. Stated in more technical mathematical lan- 
guage, this means that there exists an indirectly verified, axio- 
matically constructed theory whose postulates (1) specify a 
state-function, the independent variables of which completely 
define the state of the system at any specific instant of time, and 
(2) provide a time-equation relating the numerical empirical 
values of the independent variables of this function at any earlier 
time t 1 to their numerical empirical values at any specific later 



time t 2 in such a way that by introducing the operationally de- 
termined t 1 set of numbers into the time-equation the future t 2 
numbers can be deduced by merely solving the equation. When 
this is the case, the temporal relation between states is said to 
exemplify mechanical causation. 

It is to be noted that this definition of mechanical causality\ 
leaves open the question of what independent variables are re- 
quired to define the state of the system at any given time. Hence, 
at least two possibilities arise: (a) the concept of probability 
may be used to define the state of the system or (b) it may not 
be so used. When (b) is the case no independent variables re- 
ferring to probabilities appear in the state-function and the 
stronger type of mechanical causality is present. When (a) is 
the case independent variables referring to probabilities, as well 
as to other properties such as position and momentum, appear 
in the state-function and only the weaker type of mechanical 
causation occurs. If the reader keeps these two meanings of me- 
chanical causation in mind and makes sure which meaning 
Heisenberg is referring to in any particular sentence of this book, 
he should be able to get its answer to the question concerning the 
status of causality in modern physics. 

What of determinism? Again, there is no agreed-upon conven- 
tion among physicists and philosophers of science about how 
this word is to be used. It is in accord with the common-sense 
usage to identify it with the strongest possible causality. Let us, 
then, use the word 'determinism' to denote only the stronger 
type of mechanical causation. Then I believe the careful reader 
of this book will get the following answer to his question: In 
Newtonian, Einsteinian and quantum mechanics, mechanical, 
rather than teleological, causality holds. This is why quantum 
physics is called quantum mechanics, rather than quantum 
teleologies. But, whereas causality in Newton's and Einstein's 
physics is of the stronger type and, hence, both mechanical and 
deterministic, in quantum mechanics it is of the weaker causal 
type and, hence, mechanical but not deterministic. From the 
latter fact it follows that if anywhere in this book Heisenberg 
uses the words 'mechanical causality' in their stronger, deter- 
ministic meaning and the question be asked 'Does mechanical 
causation in this stronger meaning hold in quantum mechanics?' 



then the answer has to be 'No'. 

The situation is even more complicated, as the reader will find, 
than even these introductory distinctions between the different 
types of causation indicate. It is to be hoped, however, that this 
focusing of attention upon these different meanings will enable 
the reader to find his way through this exceptionally important 
book more easily than would otherwise be the case. 

These distinctions should suffice, also, to enable one to grasp 
the tremendous philosophical significance of the introduction of 
the weaker type of mechanical causation into modern physics, 
which has occurred in quantum mechanics. Its significance con- 
sists in reconciling the concept of objective, and in this sense 
ontological, potentiality of Aristotelian physics with the concept 
of mechanical causation of modern physics. 

It would be an error, therefore, if the reader, from Heisen- 
berg's emphasis upon the presence in quantum mechanics 
of something analogous to Aristotle's concept of potentiality, 
concluded that contemporary physics has taken us back to 
Aristotle's physics and ontology. It would be an equal error con- 
versely to conclude, because mechanical causation in its weaker 
meaning still holds in quantum mechanics, that all is the same 
now in modern physics with respect to its causality and ontology 
as was the case before quantum mechanics came into being. 
What has occurred is that in quantum theory contemporary 
man has moved on beyond the classical medieval and the modern 
world to a new physics and philosophy which combines con- 
sistently some of the basic causal and ontological assumptions 
of each. Here, let it be recalled, we use the word 'ontological' 
to denote any experimentally verified concept of scientific theory 
which refers to the object of scientific knowledge rather than 
merely to the epistemological relation of the scientist as knower 
to the object which he knows. Such an experimentally verified 
philosophical synthesis of ontological potentiality with ontolog- 
ical mechanical causality, in the weaker meaning of the latter 
concept, occurred when physicists found it impossible to account 
theoretically for the Compton effect and the results of experi- 
ment on black-body radiation unless they extended the concept 
of probability from its Newtonian and Einsteinian merely epis- 
temological, theory-of -errors role in specifying when their theory 


is or is not experimentally confirmed to the ontological role, 
specified in principle in the theory's postulates, of characterizing 
the object of scientific knowledge itself. 

Need one wonder that Heisenberg went through the subjective 
emotional experiences described in this book before he became 
reconciled to the necessity, imposed by both experimental and * 
mathematical considerations, of modifying the philosophical and 
scientific beliefs of both medieval and modern man in so deep- 
going a manner. Those interested in a firsthand description of 
the human spirit in one of its most creative moments will want 
to read this book because of this factor alone. The courage which 
it took to make this step away from the unqualified determinism 
of classical modern physics may be appreciated if one recalls that 
even such a daring, creative spirit as Einstein balked. He could 
not allow God to play dice; there could not be potentiality in the 
object of scientific knowledge, as the weaker form of mechanical 
causality in quantum mechanics allows. 

Before one concludes, however, that God has become a com- 
plete gambler and that potentiality is in all objects, certain limi- 
tations which quantum mechanics places on the application of 
its weaker form of mechanical causation must be noted. To 
appreciate these qualifications the reader must note what this 
books says about (i) the Compton effect, (2) Planck's constant 
h, and (3) the uncertainty principle which is defined in terms of 
Planck's constant. 

This constant h is a number referring to the quantum of action 
of any object or system of objects. This quantum, which extends 
atomicity from matter and electricity to light and even to energy 
itself, is very small. When the quantum numbers of the system 
being observed are small, as is the case with subatomic phe- 
nomena, then the uncertainty specified by the Heisenberg uncer- 
tainty principle of the positions and momenta of the masses of 
the system becomes significant. Then, also, the probability num- 
bers associated with the position-momentum numbers in the 
state-function become significant. When, however, the quantum 
numbers of the system are large, then the quantitative amount of 
uncertainty specified by the Heisenberg principle becomes insig- 
nificant and the probability numbers in the state-function can be 
neglected. Such is the case with gross common-sense objects. At 


this point quantum mechanics with its basically weaker type of 
causality gives rise, as a special case of itself, to Newtonian and 
Einsteinian mechanics with their stronger type of causality 
and determinism. Consequently, for human beings considered 
merely as gross common-sense objects the stronger type of 
causality holds and, hence, determinism reigns also. 

Nevertheless, subatomic phenomena are scientifically signifi- 
cant in man. To this extent, at least, the causality governing him 
is of the weaker type, and he embodies both mechanical fate and 
potentiality. There are scientific reasons for believing that this 
occurs even in heredity. Any reader who wants to pursue this 
topic beyond the pages of this book should turn to What Is Life* 
by Professor Erwin Schrodinger, the physicist after whom the 
time-equation in quantum mechanics is named. Undoubtedly, 
potentiality and the weaker form of causality hold also for 
countless other characteristics of human beings, particularly for 
those cortical neural phenomena in man that are the epistemic 
correlates of directly introspected human ideas and purposes. 

If the latter possibility is the case, the solution of a baffling 
scientific, philosophical and even moral problem may be at hand. 
This problem is: How is the mechanical causation, even in its 
weaker form, of quantum mechanics to be reconciled with the 
teleological causation patently present in the moral, political and 
legal purposes of man and in the teleological causal determina- 
tion of his bodily behaviour, in part at least, by these purposes? 
In short, how is the philosophy of physics expounded in this 
book by Heisenberg to be reconciled with moral, political and 
legal science and philosophy? 

It may help the reader to appreciate why this book must be 
mastered before these larger questions can be correctly under- 
stood or effectively answered if very brief reference is made here 
to some articles which relate its theory of physical causation to 
the wider relation between mechanism and teleology in the 
humanities and the social sciences. The relevant articles are (a) 
by Professors Rosenblueth, Wiener and Bigelow in the journal 
of The Thilosophy of Science for January, 1943; (b) by Doctors 
McCulloch and Pitts in The Bulletin of Mathematical Bio-physics, 

* University Press, Cambridge; Macmillan Company, New York; 1946. 



Volume 5, 1943, and Volume 9, 1947; and (c) Chapter XIX of 
Ideological Differences and World Order, edited by the writer 
of this Introduction and published by the Yale University Press 
in 1949. If read after this book, (a) will show how teleological 
causality arises as a special case of the merchanical causality 
described by Heisenberg here. Similarly, (b) will provide a * 
physical theory of the neurological correlates of introspected 
ideas, expressed in terms of the ideologically mechanical causal- 
ity of (a) , thereby giving an explanation of how ideas can have a 
causally significant effect on the behaviour of men. Likewise, 
(c) will show how the ideas and purposes of moral, political and 
legal man relate, by way of (b) and (a) , to the theory of physical 
potentiality and mechanical causality so thoroughly described 
by Heisenberg in this book. 

It remains to call attention to what Professor Heisenberg says 
about Bohr's principle of complementarity. This principle plays 
a great role in the interpretation of quantum theory by 'the 
Copenhagen School' to which Bohr and Heisenberg belong. 
Some students of quantum mechanics, such as Margenau in his 
book The Nature of Physical Reality*, are inclined to the con- 
clusion that quantum mechanics requires merely its definition of 
state, its Schrodinger time-equation and those other of its mathe- 
matical postulates which suffice to ensure, as noted above, that 
Einsteinian and Newtonian mechanics come out of quantum 
mechanics as one of its special cases. According to the latter 
thesis, the principle of complementarity arises from the failure 
to keep the stronger and weaker form of mechanical causality 
continuously in mind, with the resultant attribution of the 
stronger form to those portions of quantum mechanics where 
only the weaker form is involved. When this happens, the prin- 
ciple of complementarity has to be introduced to avoid 
contradiction. If, however, one avoids the foregoing practice, 
the principle of complementarity becomes, if not unnecessary, at 
least of a form such that one avoids the danger, noted by 
Margenau** and appreciated by Bohr, of giving pseudo solutions 

* McGraw Hill Book Co., Inc., New York, 1950, pp. 418-22. See also Northrop, 
The Logic of the Sciences and the Humanities, Macmillan, New York, 
1947. Chapter XI. 

** Margenau, op. cit., p. 422. 


to physical and philosophical problems by playing fast and loose 
with the law of contradiction, in the name of the principle of 

By its use the qualifications that had to be put on both the 
particle-picture common-sense language of atomic physics and 
its common-sense wave-picture language were brought together. 
But once having formulated the result with axiomatically 
constructed mathematical exactitude, any further use of it is 
merely a superficial convenience when, leaving aside the exact 
and essential mathematical assumptions of quantum mechanics, 
one indulges in the common-sense language and images of waves 
and particles. 

It has been necessary to go into the different interpretations 
of the principle of complementarity in order to enable the reader 
to pass an informed judgment concerning what Heisenberg says 
in this book about the common-sense and Cartesian concepts of 
material and mental substances. This is the case because his 
conclusion concerning Descartes results from his generalization 
of the principle of complementarity beyond physics, first, to 
the relation between common-sense biological concepts and 
mathematical physical concepts and, second, to the body-mind 
problem. The result of this generalization is that the Cartesian 
theory of mental substances comes off very much better in this 
book, as does the concept of substance generally, than is the 
case in any other book on the philosophy of contemporary 
physics which this writer knows. 

Whitehead, for example, concluded that contemporary 
science and philosophy find no place for, and have no need of, 
the concept of substance. Neutral monists such as Lord Russell 
and logical positivists such as Professor Carnap agree. 

Generally speaking, Heisenberg argues that there is no 
compelling reason to throw away any of the common-sense 
concepts of either biology or mathematical physics, after one 
knows the refined concepts that lead to the complete clarification 
of the problems in atomic physics. Because the latter clarification 
is complete, it is relevant only to a very limited range of problems 
within science and cannot enable us to avoid using many con- 
cepts at other places that would not stand critical analysis of the 
type carried out in quantum theory. Since the ideal of complete 



clarification cannot be achieved — and it is important that we 
should not be deceived about this point — one may indulge in the 
usage of common-sense concepts if it is done with sufficient care 
and caution. In this respect, certainly, complementarity is a very 
useful scientific concept. 

In any event, two things seem clear and make what Heisen- l 
berg says on these matters exceedingly important. First, the 
principle of complementarity and the present validity of the 
Cartesian and common-sense concepts of body and mind stand 
and fall together. Second, it may be that both these notions are 
merely convenient stepladders which should now be, or must 
eventually be, thrown away. Even so, in the case of the theory of 
mind at least, the stepladder will have to remain until by its use 
we find the more linguistically exact and empirically satisfactory 
theory that will permit us to throw the Cartesian language away. 
To be sure, piecemeal theories of mind which do not appeal to the 
notion of substance now exist, but none of their authors, unless it 
be Whitehead, has shown how the language of this piecemeal 
theory can be brought into commensurate and compatible rela- 
tionship with the scientific language of the other facts of human 
knowledge. It is likely, therefore, that anyone, whether he be 
a professional physicist or philosopher or the lay reader, who 
may think he knows better than Heisenberg on these important 
matters, runs the grave risk of supposing he has a scientific 
theory of mind in its relation to body, when in fact this is not 
the case. 

Up to this point we have directed attention, with but two ex- 
ceptions, to what the philosophy of contemporary physics has to 
say about the object of scientific knowledge qua object, inde- 
pendent of its relation to the scientist as knower. In short, we 
have been concerned with its ontology. This philosophy also has 
its epistemological component. This component falls into three 
parts: (i) The relation between (a) the directly observed data 
given to the physicist as inductive knower in his observations or 
his experiments and (b) the speculatively proposed, indirectly 
verified, axiomatically constructed postulates of his theory. The 
latter term (b) defines the objects of scientific knowledge qua 
object and, hence, gives the ontology. The relation between (a) 
and (b) defines one factor in the epistemology. (2) The role of 


the concept of probability in the theory of errors, by means of 
which the physicist defines the criterion for judging how far his 
experimental findings can depart, due to errors of human ex- 
perimentation, from the deduced consequences of the postulates 
of the theory and still be regarded as confirming the theory. (3) 
The effect of the experiment being performed upon the object 
being known. What Heisenberg says about the first and second 
of these three epistemological factors in contemporary physics 
has already been emphasized in this Introduction. It remains to 
direct the reader's attention to what he says about item (3) 

In modern physical theory, previous to quantum mechanics, 
(3) played no role whatever. Hence, the epistemology of modern 
physics was then completely specified by (1) and (2) alone. In 
quantum mechanics, however, (3) (as well as (1) and (2)) 
becomes very important. The very act of observing alters the 
object being observed when its quantum numbers are small. 

From this fact Heisenberg draws a very important conclusion 
concerning the relation between the object, the observing 
physicist, and the rest of the universe. This conclusion can be 
appreciated if attention is directed to the following key points. 
It may be recalled that in some of the definitions of mechanical 
causality given earlier in this Introduction, the qualifying words 
'for an isolated system' were added; elsewhere it was implicit. 
This qualifying condition can be satisfied in principle in New- 
tonian and Einsteinian mechanics, and also in practice by mak- 
ing more and more careful observations and refinements in 
one's experimental instruments. The introduction of the con- 
cept of probability into the definition of state of the object of 
scientific knowledge in quantum mechanics rules out, however, 
in principle, and not merely in practice due to the imperfec- 
tions of human observation and instruments, the satisfying of 
the condition that the object of the physicist's knowledge is an 
isolated system. Heisenberg shows also that the including of the 
experimental apparatus and even of the eye of the observing 
scientist in the physical system which is the object of the 
knower's knowledge does not help, since, if quantum mechanics 
be correct, the states of all objects have to be defined in prin- 
ciple by recourse to the concept of probability. Consequently, 
only if the whole universe is included in the object of scientific 





knowledge can the qualifying condition 'for an isolated system' 
be satisfied for even the weaker form of mechanical causation. 
Clearly, the philosophy of contemporary physics is shown by 
this book to be as novel in its epistemology as it is in its 
ontology. Indeed, it is from the originality of its ontology — 
the consistent unification of potentiality and mechanical \ 
causality in its weaker form — that the novelty of epistemology 

Unquestionably, one other thing is clear. An analysis of the 
specific experimentally verified theories of modern physics with 
respect to what they say about the object of human knowledge 
and its relation to the human knower exhibits a very rich and 
complex ontological and epistemological philosophy which is 
an essential part of the scientific theory and method itself. 
Hence, physics is neither epistemologically nor ontologically 
neutral. Deny any one of the epistemological assumptions of the 
physicist's theory and there is no scientific method for testing 
whether what the theory says about the physical object is true, 
in the sense of being empirically confirmed. Deny any one of the 
ontological assumptions and there is not enough content in 
the axiomatically constructed mathematical postulates of the 
physicist's theory to permit the deduction of the experimental 
facts which it is introduced to predict, co-ordinate consistently 
and explain. Hence, to the extent that experimental physicists 
assure us that their theory of contemporary physics is indirectly 
and experimentally verified, they ipso facto assure us that its 
rich and complex ontological and epistemological philosophy is 
verified also. 

When such empirically verified philosophy of the true in the 
natural sciences is identified with the criterion of the good and 
the just in the humanities and the social sciences, one has 
natural-law ethics and jurisprudence. In other words, one has a 
scientifically meaningful cognitive criterion and method for 
judging both the verbal, personal and social norms of the positive 
law and the living ethos embodied in the customs, habits and 
traditional cultural institutions of the de facto peoples and 
cultures of the world. It is the coming together of this new 
philosophy of physics with the respective philosophies of culture 
of mankind that is the major event in today's and tomorrow's 

world. At this point, the philosophy of physics in this book and 
its important reference to the social consequences of physics 
come together. 

The chapters of this book have been read as Gifford Lectures 
at the University of St. Andrews during the winter term 1955- 
1956. According to the will of their founder the Gifford Lectures 
should 'freely discuss all questions about man's conceptions of 
God or the Infinite, their origin, nature, and truth, whether he 
can have any such conceptions, whether God is under any or 
what limitations and so on.' The lectures of Heisenberg do not 
attempt to reach these most general and most difficult problems. 
But they try to go far beyond the limited scope of a special 
science into the wide field of those general human problems that 
have been raised by the enormous recent development and the 
far-reaching practical applications of natural science. 

An Old and a New Tradition 

WHEN one speaks today of modern physics, the first thought 
is of atomic weapons. Everybody realizes the enormous influence 
of these weapons on the political structure of our present world 
and is willing to admit that the influence of physics on the 
general situation is greater than it ever has been before. But is 
the political aspect of modern physics really the most important 
one? When the world has adjusted itself in its political structure 
to the new technical possibilities, what then will remain of the 
influence of modern physics? 

To answer these questions, one has to remember that every 
tool carries with it the spirit by which it has been created. Since 
every nation and every political group has to be interested in the 
new weapons in some way irrespective of the location and of the 
cultural tradition of this group, the spirit of modern physics will 
penetrate into the minds of many people and will connect itself 
in different ways with the older traditions. What will be the out- 
come of this impact of a special branch of modern science on 
different powerful old traditions? In those parts of the world in 
which modern science has been developed the primary interest 
has been directed for a long time toward practical activity, 
industry and engineering combined with a rational analysis of 
the outer and inner conditions for such activity. Such people will 
find it rather easy to cope with the new ideas since they have 
had time for a slow and gradual adjustment to the modern 
scientific methods of thinking. In other parts of the world these 
ideas would be confronted with the religious and philosophical 
foundations of the native culture. Since it is true that the results 
of modern physics do touch such fundamental concepts as 
reality, space and time, the confrontation may lead to entirely 



new developments which cannot yet be foreseen. One character- 
istic feature of this meeting between modern science and the 
older methods of thinking will be its complete internationality. 
In this exchange of thoughts the one side, the old tradition, will 
be different in the different parts of the world, but the other side 
will be the same everywhere and therefore the results of this 
exchange will be spread over all areas in which the discussions 
take place. 

For such reasons it may not be an unimportant task to try to 
discuss these ideas of modern physics in a not too technical 
language, to study their philosophical consequences, and to com- 
pare them with some of the older traditions. 

The best way to enter into the problems of modern physics 
may be by a historical description of the development of quan- 
tum theory. It is true that quantum theory is only a small sector 
of atomic physics and atomic physics again is only a very small 
sector of modern science. Still it is in quantum theory that the 
most fundamental changes with respect to the concept of reality 
have taken place, and in quantum theory in its final form the 
new ideas of atomic physics are concentrated and crystallized. 
The enormous and extremely complicated experimental equip- 
ment needed for research in nuclear physics shows another very 
impressive aspect of this part of modern science. But with regard 
to the experimental technique nuclear physics represents the 
extreme extension of a method of research which has determined 
the growth of modern science ever since Huyghens or Volta or 
Faraday. In a similar sense the discouraging mathematical com- 
plication of some parts of quantum theory may be said to repre- 
sent the extreme consequence of the methods of Newton or 
Gauss or Maxwell. But the change in the concept of reality 
manifesting itself in quantum theory is not simply a continuation 
of the past; it seems to be a real break in the structure of modern 
science. Therefore, the first of the following chapters will be 
devoted to the study of the historical development of quantum 



The History of Quantum Theory 

THE origin of quantum theory is connected with a well-known 
phenomenon, which did not belong to the central parts of atomic 
physics. Any piece of matter when it is heated starts to glow, 
gets red hot and white hot at higher temperatures. The colour 
does not depend much on the surface of the material, and for a 
black body it depends solely on the temperature. Therefore, the 
radiation emitted by such a black body at high temperatures is 
a suitable object for physical research; it is a simple phenomenon 
that should find a simple explanation in terms of the known laws 
for radiation and heat. The attempt made at the end of the 
nineteenth century by Lord Rayleigh and Jeans failed, however, 
and revealed serious difficulties. It would not be possible to 
describe these difficulties here in simple terms. It must be 
sufficient to state that the application of the known laws did not 
lead to sensible results. When Planck, in 1895, entered this line 
of research he tried to turn the problem from radiation to the 
radiating atom. This turning did not remove any of the difficulties 
inherent in the problem, but it simplified the interpretation of 
the empirical facts. It was just at this time, during the summer 
of 1900, that Curlbaum and Rubens in Berlin had made very 
accurate new measurements of the spectrum of heat radiation. 
When Planck heard of these results he tried to represent them 
by simple mathematical formulas which looked plausible from 
his research on the general connection between heat and 
radiation. One day Planck and Rubens met for tea in Planck's 
home and compared Rubens' latest results with a new formula 
suggested by Planck. The comparison showed a complete agree- 
ment. This was the discovery of Planck's law of heat radiation. 
It was at the same time the beginning of intense theoretical 

work for Planck. What was the correct physical interpretation 
of the new formula? Since Planck could, from his earlier work, 
translate his formula easily into a statement about the radiating 
atom (the so-called oscillator), he must soon have found that 
his formula looked as if the oscillator could only contain discrete 
quanta of energy — a result that was so different from anything 
known in classical physics that he certainly must have refused 
to believe it in the beginning. But in a period of most intensive 
work during the summer of 1900 he finally convinced himself 
that there was no way of escaping from this conclusion. It was 
told by Planck's son that his father spoke to him about his new 
ideas on a long walk through the Grunewald, the wood in the 
suburbs of Berlin. On this walk he explained that he felt he had 
possibly made a discovery of the first rank, comparable perhaps 
only to the discoveries of Newton. So Planck must have realized 
at this time that his formula had touched the foundations of our 
description of nature, and that these foundations would one day 
start to move from their traditional present location toward a 
new and as yet unknown position of stability. Planck, who was 
conservative in his whole outlook, did not like this consequence 
at all, but he published his quantum hypothesis in December of 

The idea that energy could be emitted or absorbed only in 
discrete energy quanta was so new that it could not be fitted into 
the traditional framework of physics. An attempt by Planck to 
reconcile his new hypothesis with the older laws of radiation 
failed in the essential points. It took five years until the next step 
could be made in the new direction. 

This time it was the young Albert Einstein, a revolutionary 
genius among the physicists, who was not afraid to go further 
away from the old concepts. There were two problems in which 
he could make use of the new ideas. One was the so-called 
photoelectric effect, the emission of electrons from metals under 
the influence of light. The experiments, especially those of 
Lenard, had shown that the energy of the emitted electrons did 
not depend on the intensity of the light, but only on its colour cr . 
more precisely, on its frequency. This could not be understood 
on the basis of the traditional theory of radiation. Einstein could 
explain the observations by interpreting Planck's hypothesis as 


saying that light consists of quanta of energy travelling through 
space. The energy of one light quantum should, in agreement 
with Planck's assumptions, be equal to the frequency of the light 
multiplied by Planck's constant. 

The other problem was the specific heat of solid bodies. The 
traditional theory led to values for the specific heat which fitted 
the observations' at higher temperatures but disagreed with them 
at low ones. Again Einstein was able to show that one could 
understand this behaviour by applying the quantum hypothesis 
to the elastic vibrations of the atoms in the solid body. These 
two results marked a very important advance, since they re- 
vealed the presence of Planck's quantum of action — as his con- 
stant is called among the physicists — in several phenomena, 
which had nothing immediately to do with heat radiation. They 
revealed at the same time the deeply revolutionary character of 
the new hypothesis, since the first of them led to a description of 
light completely different from the traditional wave picture. 
Light could either be interpreted as consisting of electromag- 
netic waves, according to Maxwell's theory, or as consisting of 
light quanta, energy packets travelling through space with high 
velocity. But could it be both? Einstein knew, of course, that the 
well-known phenomena of diffraction and interference can be 
explained only on the basis of the wave picture. He was not able 
to dispute the complete contradiction between this wave picture 
and the idea of the light quanta; nor did he even attempt to 
remove the inconsistency of this interpretation. He simply took 
the contradiction as something which would probably be under- 
stood only much later. 

In the meantime the experiments of Becquerel, Curie and 
Rutherford had led to some clarification concerning the struc- 
ture of the atom. In 191 1 Rutherford's observations on the inter- 
action of a-rays penetrating through matter resulted in his 
famous atomic model. The atom is pictured as consisting of a 
nucleus, which is positively charged and contains nearly the total 
mass of the atom, and electrons, which circle around the nucleus 
like the planets circle around the sun. The chemical bond be- 
tween atoms of different elements is explained as an interaction 
between the outer electrons of the neighbouring atoms; it has not 
directly to do with the atomic nucleus. The nucleus determines 



the chemical behaviour of the atom through its charge which in 
turn fixes the number of electrons in the neutral atom. Initially 
this model of the atom could not explain the most characteristic 
feature of the atom, its enormous stability. No planetary system 
following the laws of Newton's mechanics would ever go back 
to its original configuration after a collision with another such 
system. But an atom of the element carbon, for instance, will 
still remain a carbon atom after any collision or interaction in 
chemical binding. 

The explanation for this unusual stability was given by Bohr 
in 1913, through the application of Planck's quantum hypo- 
thesis. If the atom can change its energy only by discrete energy 
quanta, this must mean that the atom can exist only in discrete 
stationary states, the lowest of which is the normal state of the 
atom. Therefore, after any kind of interaction the atom will 
finally always fall back into its normal state. 

By this application of quantum theory to the atomic model, 
Bohr could not only explain the stability of the atom but also, in 
some simple cases, give a theoretical interpretation of the line 
spectra emitted by the atoms after the excitation through electric 
discharge or heat. His theory rested upon a combination of 
classical mechanics for the motion of the electrons with quantum 
conditions, which were imposed upon the classical motions for 
defining the discrete stationary states of the system. A consistent 
mathematical formulation for those conditions was later given 
by Sommerfeld. Bohr was well aware of the fact that the quan- 
tum conditions spoil in some way the consistency of Newtonian 
mechanics. In the simple case of the hydrogen atom one could 
calculate from Bohr's theory the frequencies of the light emitted 
by the atom, and the agreement with the observations was per- 
fect. Yet these frequencies were different from the orbital 
frequencies and their harmonics of the electrons circling around 
the nucleus, and this fact showed at once that the theory was still 
full of contradictions. But it contained an essential part of the 
truth. It did explain qualitatively the chemical behaviour of the 
atoms and their line spectra; the existence of the discrete station- 
ary states was verified by the experiments of Franck and Hertz, 
Stern and Gerlach. 

Bohr's theory had opened up a new line of research. The great 


amount of experimental material collected by spectroscopy 
through several decades was now available for information 
about the strange quantum laws governing the motions of the 
electrons in the atom. The many experiments of chemistry could 
be used for the same purpose. It was from this time on that the 
physicists learned to ask the right questions; and asking the right 
question is' frequently more than halfway to the solution of the 

What were these questions? Practically all of them had to do 
with the strange apparent contradictions between the results of 
different experiments. How could it be that the same radiation 
that produces interference patterns, and therefore must consist 
of waves, also produces the photoelectric effect, and therefore 
must consist of moving particles? How could it be that the fre- 
quency of the orbital motion of the electron in the atom does not 
show up in the frequency of the emitted radiation? Does this 
mean that there is no orbital motion? But if the idea of orbital 
motion should be incorrect, what happens to the electrons in- 
side the atom? One can see the electrons move through a cloud 
chamber, and sometimes they are knocked out of an atom; why 
should they not also move within the atom? It is true that they 
might be at rest in the normal state of the atom, the state of 
lowest energy. But there are many states of higher energy, where 
the electronic shell has an angular momentum. There the elec- 
trons cannot possibly be at rest. One could add a number of 
similar examples. Again and again one found that the attempt 
to describe atomic events in the traditional terms of physics led 
to contradictions. 

Gradually, during the early twenties', the physicists became 
accustomed to these difficulties, they acquired a certain vague 
knowledge about where trouble would occur, and they learned 
to avoid contradictions. They knew which description of an 
atomic event would be the correct one for the special experiment 
under discussion. This was not sufficient to form a consistent 
general picture of what happens in a quantum process, but it 
changed the minds of the physicists in such a way that they 
somehow got into the spirit of quantum theory. Therefore, even 
some time before one had a consistent formulation of quantum 
theory one knew more or less what would be the result of any 




One frequently discussed what one called ideal experiments. 
Such experiments were designed to answer a very critical ques- 
tion irrespective of whether or not they could actually be carried 
out. Of course it was important that it should be possible in 
principle to carry out the experiment, but the technique might 
be extremely complicated. These ideal experiments could be 
very useful in clarifying certain problems. If there was no agree- 
ment among the physicists about the result of such an ideal ex- 
periment, it was frequently possible to find a similar but simpler 
experiment that could be carried out, so that the experimental 
answer contributed essentially to the clarification of quantum 

The strangest experience of those years was that the paradoxes 
of quantum theory did not disappear during this process of 
clarification; on the contrary, they became even more marked 
and more exciting. There was, for instance, the experiment of 
Compton on the scattering of X-rays. From earlier experiments 
on the interference of scattered light there could be no doubt 
that scattering takes place essentially in the following way: The 
incident light wave makes an electron in the beam vibrate in 
the frequency of the wave; the oscillating electron then emits a 
spherical wave with the same frequency and thereby produces 
the scattered light. However, Compton found in 1923 that the 
frequency of scattered X-rays was different from the frequency 
of the incident X-ray. This change of frequency could be for- 
mally understood by assuming that scattering is to be described 
as collision of a light quantum with an electron. The energy of 
the light quantum is changed during the collision; and since the 
frequency times Planck's constant should be the energy of the 
light quantum, the frequency also should be changed. But what 
happens in this interpretation of the light wave ? The two ex- 
periments — one on the interference of scattered light and the 
other on the change of frequency of the scattered light — seemed 
to contradict each other without any possibility of compromise. 

By this time many physicists were convinced that these ap- 
parent contradictions belonged to the intrinsic structure of 
atomic physics. Therefore, in 1924 de Broglie in France tried to 
extend the dualism between wave description and particle de- 





scription to the elementary particles of matter, primarily to the 
electrons. He showed that a certain matter wave could 'corre- 
spond' to a moving electron, just as a light wave corresponds to 
a moving light quantum. It was not clear at the time what the 
word 'correspond' meant in this connection. But de Broglie 
suggested that the quantum condition in Bohr's theory should 
be interpreted as a statement about the matter waves. A wave 
circling around a nucleus can for geometrical reasons only be 
a stationary wave; and the perimeter of the orbit must be an 
integer multiple of the wave length. In this way de Broglie 's idea 
connected the quantum condition, which always had been a for- 
eign element in the mechanics of the electrons, with the dualism 
between waves and particles. 

In Bohr's theory the discrepancy between the calculated 
orbital frequency of the electrons and the frequency of the 
emitted radiation had to be interpreted as a limitation to the 
concept of the electronic orbit. This concept had been somewhat 
doubtful from the beginning. For the higher orbits, however, the 
electrons should move at a large distance from the nucleus just 
as they do when one sees them moving through a cloud cham- 
ber. There one should speak about electronic orbits. It was 
therefore very satisfactory that for these higher orbits the fre- 
quencies of the emitted radiation approach the orbital frequency 
and its higher harmonics. Also Bohr had already suggested in his 
early papers that the intensities of the emitted spectral lines 
approach the intensities of the corresponding harmonics. This 
principle of correspondence had proved very useful for the ap- 
proximative calculation of the intensities of spectral lines. In this 
way one had the impression that Bohr's theory gave a qualitative 
but not a quantitative description of what happens inside the 
atom; that some new feature of the behaviour of matter was 
qualitatively expressed by the quantum conditions, which in 
turn were connected with the dualism between waves and par- 

The precise mathematical formulation of quantum theory 
finally emerged from two different developments. The one 
started from Bohr's principle of correspondence. One had to give 
up the concept of the electronic orbit, but still had to maintain it 
in the limit of high quantum numbers, i.e., for the large orbits. 

In this latter case the emitted radiation, by means of its fre- 
quencies and intensities, gives a picture of the electronic orbit; 
it represents what the mathematicians call a Fourier expansion 
of the orbit. The idea suggested itself that one should write down 
the mechanical laws not as equations for the positions and 
velocities of the electrons but as equations for the frequencies 
and amplitudes of their Fourier expansion. Starting from such 
equations and changing them very little one could hope to come 
to relations for those quantities which correspond to the fre- 
quencies and intensities of the emitted radiation, even for the 
small orbits and the ground state of the atom. This plan could 
actually be carried out; in the summer of 1925 it led to a 
mathematical formalism called matrix mechanics or, more 
generally, quantum mechanics. The equations of motion in 
Newtonian mechanics were replaced by similar equations be- 
tween matrices; it was a strange experience to find that many of 
the old results of Newtonian mechanics, like conservation of 
energy, etc., could be derived also in the new scheme. Later the 
investigations of Born, Jordan and Dirac showed that the 
matrices representing position and momentum of the electron 
did not commute. This latter fact demonstrated clearly the essen- 
tial difference between quantum mechanics and classical me- 

The other development followed de Broglie's idea of matter 
waves. Schrodinger tried to set up a wave equation for de 
Broglie's stationary waves around the nucleus. Early in 1926 he 
succeeded in deriving the energy values of the stationary states 
of the hydrogen atom as 'Eigenvalues' of his wave equation 
and could give a more general prescription for transforming a 
given set of classical equations of motion into a corresponding 
wave equation in a space of many dimensions. Later he was able 
to prove that his formalism of wave mechanics was mathemati- 
cally equivalent to the earlier formalism of quantum mechanics. 

Thus one finally had a consistent mathematical formalism, 
which could be defined in two equivalent ways starting either 
from relations between matrices or from wave equations. This 
formalism gave the correct energy values for the hydrogen atom; 
it took less than one year to show that it was also successful for 
the helium atom and the more complicated problems of the 






■ "-^V 

heavier atoms. But in what sense did the new formalism describe 
the atom? The paradoxes of the dualism between wave picture 
and particle picture were not solved; they were hidden somehow 
in the mathematical scheme. 

A first and very interesting step toward a real understanding 
of quantum theory was taken by Bohr, Kramers and Slater in 
1924. These authors tried to solve the apparent contradiction 
between the wave picture and the particle picture by the concept 
of the probability wave. The electromagnetic waves were in- 
terpreted not as 'real' waves but as probability waves, the in- 
tensity of which determines in every point the probability for 
the absorption (or induced emission) of a light quantum by an 
atom at this point. This idea led to the conclusion that the laws ' 
of conservation of energy and momentum need not be true for 
the single event, that they are only statistical laws and are true 
only in the statistical average. This conclusion was not correct, 
however, and the connections between the wave aspect and the 
particle aspect of radiation were still more complicated. 

But the paper of Bohr, Kramers and Slater revealed one es- 
sential feature of the correct interpretation of quantum theory. 
This concept of the probability wave was something entirely new 
in theoretical physics since Newton. Probability in mathematics 
or in statistical mechanics means a statement about our degree 
of knowledge of the actual situation. In throwing dice we do not 
know the fine details of the motion of our hands which de- 
termine the fall of the dice and therefore we say that the proba- 
bility for thrownig a special number is just one in six. The 
probability wave of Bohr, Kramers, Slater, however, meant 
more than that; it meant a tendency for something. It was a I 
quantitative version of the old concept of 'potentia' in Aris- 
totelian philosophy. It introduced something standing in the 
middle between the idea of an event and the actual event, a 
strange kind of physical reality just in the middle between pos- 
sibility and reality. 

Later when the mathematical framework of quantum theory 
was fixed, Born took up this idea of the probability wave and 
gave a clear definition of the mathematical quantity in the 
formalism, which was to be interpreted as the probability wave. 
It was not a three-dimensional wave like elastic or radio waves, 

but a wave in the many-dimensional configuration space, and 
therefore a rather abstract mathematical quantity. 

Even at this time, in the summer of 1926, it was not clear in 
every case how the mathematical formalism should be used to 
describe a given experimental situation. One knew how to de- 
scribe the stationary states of an atom, but one did not know 
how to describe a much simpler event — as for instance an elec- 
tron moving through a cloud chamber. 

When Schrodinger in that summer had shown that his formal- 
ism of wave mechanics was mathematically equivalent to quan- 
tum mechanics he tried for some time to abandon the idea of 
quanta and 'quantum jumps' altogether and to replace the 
electrons in the atoms simply by his three-dimensional matter 
waves. He was inspired to this attempt by his result, that the 
energy levels of the hydrogen atom in his theory seemed to be 
simply the eigenfrequencies of the stationary matter waves. 
Therefore, he thought it was a mistake to call them energies: 
they were just frequencies. But in the discussions which took 
place in the autumn of 1926 in Copenhagen between Bohr and 
Schrodinger and the Copenhagen group of physicists it soon 
became apparent that such an interpretation would not even be 
sufficient to explain Planck's formula of heat radiation. 

During the months following these discussions an intensive 
study of all questions concerning the interpretation of quantum 
theory in Copenhagen finally led to a complete and, as many 
physicists believe, satisfactory clarification of the situation. But 
it was not a solution which one could easily accept. I remember 
discussions with Bohr which went through many hours till very 
late at night and ended almost in despair; and when at the end 
of the discussion I went alone for a walk in the neighbouring 
park I repeated to myself again and again the question : Can 
nature possibly be as absurd as it seemed to us in these atomic 
experiments ? 

The final solution was approached in two different ways. The 
one was a turning around of the question. Instead of asking: 
How can one in the known mathematical scheme express a given 
experimental situation? the other question was put: Is it true, 
perhaps, that only such experimental situations can arise in 
nature as can be expressed in the mathematical formalism? The 





assumption that this was actually true led to limitations in the 
use of those concepts that had been the basis of classical physics 
since Newton. One could speak of the position and of the 
velocity of an electron as in Newtonian mechanics and one 
could observe and measure these quantities. But one could not 
fix both quantities simultaneously with an arbitrarily high 
accuracy. Actually the product of these two inaccuracies turned 
out to be not less than Planck's constant divided by the mass of 
the particle. Similar relations could be formulated for other ex- 
perimental situations. They are usually called relations of un- 
certainty or principle of indeterminacy. One had learned that 
the old concepts fit nature only inaccurately. 

The other way of approach was Bohr's concept of comple- 
mentarity. Schrodinger had described the atom as a system not 
of a nucleus and electrons but of a nucleus and matter waves. 
This picture of the matter waves certainly also contained an ele- 
ment of truth. Bohr considered the two pictures — particle pic- 
ture and wave picture — as two complementary descriptions of 
the same reality. Any of these descriptions can be only partially 
true, there must be limitations to the use of the particle concept 1 
as well as of wave concept, else one could not avoid contra- 
dictions. If one takes into account those limitations which can be 
expressed by the uncertainty relations, the contradictions disap- 

In this way since the spring of 1927 one has had a consistent 
interpretation of quantum theory, which is frequently called the 
'Copenhagen interpretation'. This interpretation received its 
crucial test in the autumn of 1927 at the Solvay conference in 
Brussels. Those experiments which had always led to the worst 
paradoxes were again and again discussed in all details, especially 
by Einstein. New ideal experiments were invented to trace any 
possible inconsistency of the theory, but the theory was shown 
to be consistent and seemed to fit the experiments as far as one 
could see. 

The details of this Copenhagen interpretation will be the 1 
subject of the next chapter. It should be emphasized at this point 
that it has taken more than a quarter of a century to get from 
the first idea of the existence of energy quanta to a real under- 
standing of the quantum theoretical laws. This indicates the 

great change that had to take place in the fundamental concepts 
concerning reality before one could understand the new situa- 


The Copenhagen Interpretation of 
Quantum Theory 

THE Copenhagen interpretation of quantum theory starts from 
a paradox. Any experiment in physics, whether it refers to the 
phenomena of daily life or to atomic events, is to be described 
in the terms of classical physics. The concepts of classical physics 
form the language by which we describe the arrangements of \ 
our experiments and state the results. We cannot and should not 
replace these concepts by any others. Still the application of ; 
these concepts' is limited by the relations of uncertainty. We I 
must keep in mind this limited range of applicability of the classi- 1 
cal concepts while using them, but we cannot and should not try f 
to improve them. 

For a better understanding of this paradox it is useful to com- 
pare the procedure for the theoretical interpretation of anj 
experiment in classical physics and in quantum theory. In New-, 
ton's mechanics, for instance, we may start by measuring the] 
position and the velocity of the planet whose motion we are J 
going to study. The result of the observation is translated into! 
mathematics by deriving numbers for the co-ordinates and thef 
momenta of the planet from the observation. Then the equations] 
of motion are used to derive from these values of the co-ordinates i 
and momenta at a given time the values of these co-ordinates or 
any other properties of the system at a later time, and in this 
way the astronomer can predict the properties of the system at a 
later time. He can, for instance, predict the exact time for an 
eclipse of the moon. , 

In quantum theory the procedure is slightly different. We| 
could for instance be interested in the motion of an electroni 


through a cloud chamber and could determine by some kind of 
observation the initial position and velocity of the electron. But 
this determination will not be accurate; it will at least contain 
the inaccuracies following from the uncertainty relations and 
will probably contain still larger errors due to the difficulty of 
the experiment. It is the first of these inaccuracies which allows 
us to translate the result of the observation into the mathematical 
scheme of quantum theory. A probability function is written 
down which represents the experimental situation at the time 
of the measurement, including even the possible errors of the 

This probability function represents a mixture of two things, 
partly a fact and partly our knowledge of a fact. It represents a 
fact in so far as it assigns at the initial time the probability unity 
(i.e., complete certainty) to the initial situation: the electron 
moving with the observed velocity at the observed position; 
'observed' means observed within the accuracy of the experi- 
ment. It represents our knowledge in so far as another observer 
could perhaps know the position of the electron more accurately. 
The error in the experiment does — at least to some extent — not 
represent a property of the electron but a deficiency in our 
knowledge of the electron. Also this deficiency of knowledge is 
expressed in the probability function. 

In classical physics one should in a careful investigation also 
consider the error of the observation. As a result one would get 
a probability distribution for the initial values of the co-ordinates 
and velocities and therefore something very similar to the proba- 
bility function in quantum mechanics. Only the necessary un- 
certainty due to the uncertainty relations is lacking in classical 

When the probability function in quantum theory has been 
determined at the initial time from the observation, one can 
from the laws of quantum theory calculate the probability func- 
tion at any later time and can thereby determine the probability 
for a measurement giving a specified value of the measured 
quantity. We can, for instance, predict the probability for find- 
J ng the electron at a later time at a given point in the cloud 
chamber. It should be emphasized, however, that the probability 
function does not in itself represent a course of events in the 

4 8 


course of time. It represents a tendency for events and our | 
knowledge of events. The probability function can be connected 
with reality only if one essential condition is fulfilled: if a new 
measurement is made to determine a certain property of the 
system. Only then does the probability function allow us to 
calculate the probable result of the new measurement. The result 
of the measurement again will be stated in terms of classical 

Therefore, the theoretical interpretation of an experiment 
requires three distinct steps: (i) the translation of the initial 
experimental situation into a probability function; (2) the fol- 1 
lowing up of this function in the course of time; (3) the state- ■ 
ment of a new measurement to be made of the system, the result 
of which can then be calculated from the probability function. • 
For the first step the fulfillment of the uncertainty relations is a 
necessary condition. The second step cannot be described inl 
terms of the classical concepts; there is no description of what! 
happens to the system between the initial observation and thel 
next measurement. It is only in the third step that we changej 
over again from the 'possible' to the 'actual'. 

Let us illustrate these three steps in a simple ideal experiment 
It has been said that the atom consists of a nucleus and electron 
moving around the nucleus; it has also been stated that the cot 
cept of an electronic orbit is doubtful. One could argue that i 
should at least in principle be possible to observe the electroi 
in its orbit. One should simply look at the atom through ' 
•microscope of a very high revolving power, then one would se 
the electron moving in its orbit. Such a high revolving powe 
could to be sure not be obtained by a miscroscope using ordinar 
light, since the inaccuracy of the measurement of the positioi 
can never be smaller than the wave length of the light. But ' 
microscope using y-rays with a wave length smaller than the siz 
of the atom would do. Such a microscope has not yet been con- 
structed but that should not prevent us from discussing the ide" 

Is the first step, the translation of the result of the observatiol 
into a probability function, possible? It is possible only if the un 
certainty relation is fulfilled after the observation. The positioi 
of the electron will be known with an accuracy given by thi 


W ave length of the y-ray. The electron may have been practically 
at rest before the observation. But in the act of observation at 
least one light quantum of the y-ray must have passed the micro- 
scope and must first have been deflected by the electron. There- 
fore, the electron has been pushed by the light quantum, it has 
changed its momentum and its velocity, and one can show that 
the uncertainty of this change is just big enough to guarantee 
the validity of the uncertainty relations. Therefore, there is no 
difficulty with the first step. 

At the same time one can easily see that there is no way of 
observing the orbit of the electron around the nucleus. The 
second step shows a wave pocket moving not around the nucleus 
but away from the atom, because the first light quantum will 
have knocked the electron out from the atom. The momentum 
of light quantum of the y-ray is much bigger than the original 
momentum of the electron if the wave length of the y-ray is 
much smaller than the size of the atom. Therefore, the first light 
quantum is sufficient to knock the electron out of the atom and 
one can never observe more than one point in the orbit of the 
electron; therefore, there is no orbit in the ordinary sense. The 
next observation — the third step — will show the electron on its 
path from the atom. Quite generally there is no way of describ- 
ing what happens between two consecutive observations. It is 
of course tempting to say that the electron must have been 
somewhere between the two observations and that therefore the 
electron must have described some kind of path or orbit even if 
it may be impossible to know which path. This would be a 
reasonable argument in classical physics. But in quantum theory 
it would be a misuse of the language which, as we will see later, 
cannot be justified. We can leave it open for the moment, 
whether this warning is a statement about the way in which we 
should talk about atomic events or a statement about the events 
themselves, whether it refers to epistemology or to ontology. 
In any case we have to be very cautious about the wording of 
any statement concerning the behaviour of atomic particles. 

Actually we need not speak of particles at all. For many ex- 
periments it is more convenient to speak of matter waves; for 
mstance, of stationary matter waves around the atomic nucleus. 
Su ch a description would directly contradict the other descrip- 



tion if one does not pay attention to the limitations given by the 
uncertainty relations. Through the limitations the contradiction ) 
is avoided The use of 'matter waves' is convenient, for example, 1 
when dealing with the radiation emitted by the atom. By means J 
of its frequencies and intensities the radiation gives information* 
about the oscillating charge distribution in the atom, and there? 
the wave picture comes much nearer to the truth than the par- 1 
tide picture. Therefore, Bohr advocated the use of both pictures. 1 
which he called 'complementary' to each other. The two pic- f 
tures are of course mutually exclusive, because a certain thing 
cannot at the same time be a particle (i.e., substance confined to 
a very small volume) and a wave (i.e., a field spread out over a 3 
large space), but the two complement each other. By playing I 
with both pictures, by going from the one picture to the other! 
and back again, we finally get the right impression of the strange 
kind of reality behind our atomic experiments. Bohr uses the 
concept of 'complementarity' at several places in the interpre-j 
tation of quantum theory. The knowledge of the position of I 
a particle is complementary to the knowledge of its velocity orl 
momentum. If we know the one with high accuracy we cannot! 
know the other with high accuracy; still we must know both foil 
determining the behaviour of the system. The space-time descnr>- 
tion of the atomic events is complementary to their deterministic 
description. The probability function obeys an equation of 
motion as the coordinates did in Newtonian mechanics; its 
change in the course of time is completely determined by th^ 
quantum mechanical equation, but it does not allow a descnp 
tion in space and time. The observation, on the other hand.] 
enforces the description in space and time but breaks the de 
termined continuity of the probability function by changing our 
knowledge of the system. 

Generally the dualism between two different descriptions of 
the same reality is no longer a difficulty since we know from] 
the mathematical formulation of the theory that contradictions! 
cannot arise. The dualism between the two complementary pic-l 
tures _ waV es and particles— is also clearly brought out in thel 
flexibility of the mathematical scheme. The formalism is nor- 
mally written to resemble Newtonian mechanics, with equations 
of motion for the co-ordinates and the momenta of the particles. 


But by a simple transformation it can be rewritten to resemble 
a wave equation for an ordinary three-dimensional matter wave. 
Therefore, this possibility of playing with different comple- 
mentary pictures has its analogy in the different transformations 
of the mathematical scheme; it does not lead to any difficulties 
in the Copenhagen interpretation of quantum theory. 

A real difficulty in the understanding of this interpretation 
arises, however, when one asks the famous question: But what 
happens 'really' in an atomic event? It has been said before that 
the mechanism and the results of an observation can always be 
stated in terms of the classical concepts. But what one deduces 
from an observation is a probability function, a mathematical 
expression that combines statements about possibilities or tend- 
encies with statements about our knowledge of facts. So we can- 
not completely objectify the result of an observation, we cannot 
describe what 'happens' between this observation and the next. 
This looks as if we had introduced an element of subjectivism 
into the theory, as if we meant to say: what happens depends on 
our way of observing it or on the fact that we observe it. Before 
discussing this problem of subjectivism it is necessary to explain 
quite clearly why one would get into hopeless difficulties if one 
tried to describe what happens between two consecutive ob- 

For this purpose it is convenient to discuss the following ideal 
experiment: We assume that a small source of monochromatic 
light radiates toward a black screen with two small holes in it. 
The diameter of the holes may be not much bigger than the 
wave length of the light, but their distance will be very much 
bigger. At some distance behind the screen a photographic plate 
registers the incident light. If one describes this experiment in 
terms of the wave picture, one says that the primary wave pene- 
trates through the two holes; there will be secondary spherical 
waves starting from the holes that interfere with one another, 
and the interference will produce a pattern of varying intensity 
°n the photographic plate. 

The blackening of the photographic plate is a quantum 
Process, a chemical reaction produced by single light quanta. 
Therefore, it must also be possible to describe the experiment in 
^rms of light quanta. If it would be permissible to say what 



happens to the single light quantum between its emission from, 
the light source and its absorption in the photographic plate, one! 
could argue as follows: The single light quantum can come f 
through the first hole or through the second one. If it goes ; 
through the first hole and is scattered there, its probability fori 
being absorbed at a certain point of the photographic plate can- J 
not depend upon whether the second hole is closed or open. The 
probability distribution on the plate will be the same as if only j 
the first hole was open. If the experiment is repeated many times l 
and one takes together all cases in which the light quantum nasi 
gone through the first hole, the blackening of the plate due to I 
these cases will correspond to this probability distribution. If one 
considers only those light quanta that go through the second 
hole, the blackening should correspond to a probability distribu- 
tion derived from the assumption that only the second hole is| 
open. The total blackening, therefore, should just be the sum of j 
the blackenings in the two cases; in other words, there should be* 
no interference pattern. But we know this is not correct anc 
the experiment will show the interference pattern. ThereforeJ 
the statement that any light quantum must have gone eithef 
through the first or through the second hole is problematic and 
leads to contradictions. This example shows clearly that the conj 
cept of the probability function does not allow a description o£ 
what happens between two observations. Any attempt to nndl 
such a description would lead to contradictions; this must meapi 
that the term 'happens' is restricted to the observation. 

Now, this is a very strange result, since it stems to indicate 
that the observation plays a decisive role in the event and that! 
the reality varies, depending upon whether we observe it or not.l 
To make this point clearer we have to analyze the process of 
observation more closely. j 

To begin with, it is important to remember that in natural! 
science we are not interested in the universe as a whole, includ-j 
ing ourselves, but we direct our attention to some part of the 
universe and make that the object of our studies. In atomic 
physics this part is usually a very small object, an atomic particle J 
or a group of such particles, sometimes much larger— the sizej 
does not matter; but it is important that a large part of the.? 
universe, including ourselves, does not belong to the object. 


Now, the theoretical interpretation of an experiment starts 
with the two steps that have been discussed. In the first step we 
have to describe the arrangement of the experiment, eventually 
combined with a first observation, in terms of classical physics 
and translate this description into a probability function. This 
probability function follows the laws of quantum theory, and its 
change in the course of time, which is continuous, can be calcu- 
lated from the initial conditions; this is the second step. The 
probability function combines objective and subjective elements. 
It contains statements about possibilities or better tendencies 
('potentia' in Aristotelian philosphy), and these statements 
are completely objective, they do not depend on any observer; 
and it contains statements about our knowledge of the system, 
which of course are subjective in so far as they may be different 
for different observers. In ideal cases the subjective element in 
the probability function may be practically negligible as com- 
pared with the objective one. The physicists' then speak of a 
'pure case'. 

When we now come to the next observation, the result of 
which should be predicted from the theory, it is very important 
to realize that our object has to be in contact with the other part 
of the world, namely, the experimental arrangement, the meas- 
uring rod, etc., before or at least at the moment of observation. 
This means that the equation of motion for the probability func- 
tion does now contain the influence of the interaction with the 
measuring device. This influence introduces a new element of 
uncertainty, since the measuring device is necessarily described 
in the terms of classical physics; such a description contains 
all the uncertainties concerning the miscroscopic structure of 
the device which we know from thermodynamics, and since the 
device is connected with the rest of the world, it contains in fact 
the uncertainties of the microscopic structure of the whole 
world. These uncertainties may be called objective in so far as 
they are simply a consequence of the description in the terms of 
classical physics and do not depend on any observer. They may 
fee called subjective in so far as they refer to our incomplete 
knowledge of the world. 

After this interaction has taken place, the probability function 
contains the objective element of tendency and the subjective 



element of incomplete knowledge, even if it has been been a 'pure 
case' before. It is for this reason that the result of the observa- 
tion cannot generally be predicted with certainty; what can be 
predicted is the probability of a certain result of the observation, 
and this statement about the probability can be checked by re- 
peating the experiment many times. The probability function 
d oes — unlike the common procedure in Newtonian mechanics — 
not describe a certain event but, at least during the process of 
observation, a whole ensemble of possible events. 

The observation itself changes the probability function dis- 
continuously; it selects of all possible events the actual one that 
has taken place. Since through the observation our knowledge 
of the system has changed discontinuously, its mathematical 
representation also has undergone the discontinuous change and 
we speak of a 'quantum jump'. When the old adage 'Natura 
non f acit saltus* is used as a basis for criticism of quantum theory, 
we can reply that certainly our knowledge can change suddenly < 
and that this fact justifies the use of the term 'quantum jump'. 

Therefore, the transition from the 'possible' to the 'actual' 
takes place during the act of observation. If we want to describe 
what happens in an atomic event, we have to realize that the 
word 'happens' can apply only to the observation, not to the j 
state of affairs between two observations. It applies to the 
physical, not the psychical act of observation, and we may say ; 
that the transition from the 'possible' to the 'actual' takes place i 
as soon as the interaction of the object with the measuring j 
device, and thereby with the rest of the world, has come into ' 
play; it is not connected with the act of registration of the result 
by the mind of the observer. The discontinuous change in the j 
probability function, however, takes place with the act of regis- 
tration, because it is the discontinuous change of our knowledge < 
in the instant of registration that has its image in the discontinu- 
ous change of the probability function. 

To what extent, then, have we finally come to an objective 
description of the world, especially of the atomic world? In 
classical physics science started from the belief— or should onej 
say from the illusion? — that we could describe the world or at{ 
least parts of the world without any reference to ourselves. This j 
is actually possible to a large extent. We know that the city of| 


London exists whether we see it or not. It may be said that clas- 
sical physics is just that idealization in which we can speak 
about parts of the world without any reference to ourselves. Its 
success has led to the general ideal of an objective description of 
the world. Objectivity has become the first criterion for the 
value of any scientific result. Does the Copenhagen interpreta- 
tion of quantum theory still comply with this ideal? One may 
perhaps say that quantum theory corresponds to this ideal as far 
as possible. Certainly quantum theory does not contain genuine 
subjective features, it does not introduce the mind of the physi- 
cist as a part of the atomic event. But it starts from the division 
of the world into the 'object' and the rest of the world, and 
from the fact that at least for the rest of the world we use the 
classical concepts in our description. This division is arbitrary 
and historically a direct consequence of our scientific method; 
the use of the classical concepts is finally a consequence of the 
general human way of thinking. But this is already a reference 
to ourselves and in so far our description is not completely 

It has been stated in the beginning that the Copenhagen 
interpretation of quantum theory starts with a paradox. It starts 
from the fact that we describe our experiments in the terms of 
classical physics and at the same time from the knowledge that 
these concepts do not fit nature accurately. The tension between 
these two starting points is the root of the statistical character of 
quantum theory. Therefore, it has sometimes been suggested 
that one should depart from the classical concepts altogether and 
that a radical change in the concepts used for describing the 
experiments might possibly lead back to a nonstatical, com- 
pletely objective description of nature. 

This suggestion, however, rests upon a misunderstanding. The 
concepts of classical physics are just a refinement of the concepts 
of daily life and are an essential part of the language which 
forms the basis of all natural science. Our actual situation in 
science is such that we do use the classical concepts for the 
description of the experiments, and it was the problem of quan- 
tum theory to find theoretical interpretation of the experiments 
°n this basis. There is no use in discussing what could be done if 
w e were other beings than we are. At this point we have to 



realize, as von Weizsacker has put it, that 'Nature is earlier than 
man, but man is earlier than natural science.' The first part of 
the sentence justifies classical physics, with its ideal of complete 
objectivity. The second part tells us why we cannot escape the 
paradox of quantum theory, namely, the necessity of using the 
classical concepts. 

We have to add some comments on the actual procedure in 
the quantum-theoretical interpretation of atomic events. It has! 
been said that we always start with a division of the world intoj 
an object, which we are going to study, and the rest of the world, J 
and that this division is to some extent arbitrary. It should in- 
deed not make any difference in the final result if we, e.g., addj 
some part of the measuring device or the whole device to the] 
object and apply the laws of quantum theory to this more com- 
plicated object. It can be shown that such an alteration of the 1 
theoretical treatment would not alter the predictions concerning 
a given experiment. This follows mathematically from the fad 
that the laws of quantum theory are for the phenomena in whict 
Planck's constant can be considered as a very small quantity! 
approximately identical with the classical laws. But it would bej 1 
a mistake to believe that this application of the quantum* 
theoretical laws to the measuring device could help to avoid the* 
fundamental paradox of quantum theory. 

The measuring device deserves this name only if it is in close 
contact with the rest of the world, if there is an interaction br 
tween the device and the observer. Therefore, the uncertaint 
with respect to the microscopic behaviour of the world will entet 
into the quantum-theoretical system here just as well as in the 
first interpretation. If the measuring device would be isolated 
from the rest of the world, it would be neither a measuring device 
nor could it be described in the terms of classical physics at all. 

With regard to this situation Bohr has emphasized that it i^ 
more realistic to state that the division into the object and thtf 
rest of the world is not arbitrary. Our actual situation in researcr 
work in atomic physics is usually this: we wish to understand r 
certain phenomenon, we wish to recognize how this phc 
nomenon follows from the general laws of nature. Therefore^ 
that part of matter or radiation which takes part in the phej 
nomenon is the natural 'object' in the theoretical treatment an<* 


jiould be separated in this respect from the tools used to study 
the phenomenon. This again emphasizes a subjective element in 
the description of atomic events, since the measuring device has 
bee n constructed by the observer, and we have to remember that 
what we observe is not nature in itself but nature exposed to our 
method of questioning. Our scientific work in physics consists in 
asking questions about nature in the language that we possess 
and trying to get an answer from experiment by the means that 
are at our disposal. In this way quantum theory reminds us, as 
Bohr has put it, of the old wisdom that when searching for 
harmony in life one must never forget that in the drama of 
existence we are ourselves both players and spectators. It is 
understandable that in our scientific relation to nature our own 
activity becomes very important when we have to deal with 
parts of nature into which we can penetrate only by using the 
most elaborate tools. 

Quantum Theory and the Roots of 
Atomic Science 

THE concept of the atom goes back much further than the 
ginning of modern science in the seventeenth century; it has it| 
origin in ancient Greek philosophy and was in that early perk 
the central concept of materialism taught by Leucippus an<| 
Democritus. On the other hand, the modern interpretations 
atomic events has very little resemblance to genuine materialisti| 
philosophy; in fact, one may say that atomic physics has turne 
science away from the materialistic trend it had during the nin* 
teenth century. It is therefore interesting to compare the d^ 
velopment of Greek philosophy toward the concept of the ator 
with the present position of this concept in modern physics. 

The idea of the smallest, indivisible ultimate building bloci 
of matter first came up in connection with the elaboration of th<j 
concepts of Matter, Being, and Becoming which characterize 
the first epoch of Greek philosophy. This period started in tl 
sixth century b.c. with Thales, the founder of the Milesiai 
school, to whom Aristotle ascribes the statement: 'Water is th| 
material cause of all things.* This statement, strange as it look 
to us, expresses, as Nietzsche has pointed out, three fundaments 
ideas of philosophy. First, the question as to the material caus 
of all things; second, the demand that this question be answere 
in conformity with reason, without resort to myths or mystic 
ism; third, the postulate that ultimately it must be possible td 
reduce everything to one principle. Thales' statement was thj 
first expression of the idea of a fundamental substance, of whicl 
all other things were transient forms. The word 'substance' in thij 
connection was certainly in that age not interpreted in thq 


nurely material sense which we frequently ascribe to it today. 
Life was connected with or inherent in this 'substance' and 
Aristotle ascribes to Thales also the statement: All things are full 
f gods. Still the question was put as to the material cause of 
all things and it is not difficult to imagine that Thales took his 
view primarily from meteorological considerations. Of all things 
we know water can take the most various shapes; it can in the 
winter take the form of ice and snow, it can change into vapour, 
and it can form the clouds. It seems to turn into earth where the 
rivers form their delta, and it can spring from the earth. Water 
is the condition for life. Therefore, if there was such a funda- 
mental substance, it was natural to think of water first. 

The idea of the fundamental substances was then carried 
further by Anaximander, who was a pupil of Thales and lived in 
the same town. Anaximander denied the fundamental substance 
to be water or any of the known substances. He taught that the 
primary substance was infinite, eternal and ageless and that it 
encompassed the world. This primary substance is transformed 
into the various substances with which we are familiar. Theo- 
phrastus quotes from Anaximander: 'Into that from which 
things take their rise they pass away once more, as is ordained, 
for they make reparation and satisfaction to one another for 
their injustice according to the ordering of time.' In this 
philosophy the antithesis of Being and Becoming plays the 
fundamental role. The primary substance, infinite and ageless, 
the undifferentiated Being, degenerates into the various forms 
which lead to endless struggles. The process of Becoming is con- 
sidered as a sort of debasement of the infinite Being — a dis- 
integration into the struggle ultimately expiated by a return into 
that which is without shape or character. The struggle which is 
meant here is the opposition between hot and cold, fire and 
water, wet and dry, etc. The temporary victory of the one over 
the other is the injustice for which they finally make reparation 
, ln tne ordering of time. According to Anaximander, there is 

eternal motion', the creation and passing away of worlds from 
infinity to infinity, 
ft may be interesting to notice at this point that the prob- 

ein whether the primary substance can be one of the known 
substances or must be something essentially different — occurs in 



a somewhat different form in the most modern part of atomic 

physics. The physicists today try to find a fundamental law ol 

motion for matter from which all elementary particles and therj 

properties can be derived mathematically. This fundamental 

equation of motion may refer either to waves of a known type! 

to proton and meson waves, or to waves of an essentially drfi 

ferent character which have nothing to do with any of th^ 

known waves or elementary particles. In the first case it would 

mean that all other elementary particles can be reduced in sonuj 

way to a few sorts of 'fundamental' elementary particles' 

actually theoretical physics has during the past two decade 

mostly followed this line of research. In the second case all dif 

ferent elementary particles could be reduced to some universa 

substance which we may call energy or matter, but none of tn 

different particles could be preferred to the others as being mor 

fundamental. The latter view of course corresponds to the do<j 

trine of Anaximander, and I am convinced that in moder 

physics this view is the correct one. But let us return to Gree 


The third of the Milesian philosophers, Anaximenes, an 
sociate of Anaximander, taught that air was the primary suj 
stance. 'Just as our soul, being air, holds us together, so (* 
breath and air encompass the whole world.' Anaximenes intr 
duced into the Milesian philosophy the idea that the process 
condensation or rarefaction causes the change of the prima 
substance into the other substances. The condensation of watt 
vapour into clouds was an obvious example, and of course th 
difference between water vapour and air was not known at thai 

In the philosophy of Heraclitus of Ephesus the concept 
Becoming occupies the foremost place. He regarded that whic 
moves, the fire, as the basic element. The difficulty, to reconcij 
the idea of one fundamental principle with the infinite vanetf 
of phenomena, is solved for him by recognizing that the strife c 
the opposites is really a kind of harmony. For Heraclitus th 
world is at once one and many, it is just 'the opposite tensiol 
of the opposites that constitutes the unity of the One. He sayj 
'We must know that war is common to all and strife is justice 
and that all things come into being and pass away through strife! 


Looking back to the development of Greek philosophy up to 
his point one realizes that it has been borne from the beginning 

this stage by the tension between the One and the Many. For 
t0 sen ses the world consists of an infinite variety of things and 
° nts, co iours and sounds. But in order to understand it we 
have to introduce some kind of order, and order means to recog- 
nize what is equal, it means some sort of unity. From this springs 
the belief that there is one fundamental principle, and at the 
same time the difficulty to derive from it the infinite variety of 
things. That there should be a material cause for all things was a 
natural starting point since the world consists of matter. But 
when one carried the idea of fundamental unity to the extreme 
one came to that infinite and eternal undifferentiated Being 
which, whether material or not, cannot in itself explain the 
infinite variety of things. This leads to the antithesis of Being 
and Becoming and finally to the solution of Heraclitus, that the 
change itself is the fundamental principle; the 'imperishable 
change, that renovates the world', as the poets have called it. 
But the change in itself is not a material cause and therefore is 
represented in the philosophy of Heraclitus by the fire as the 
basic element, which is both matter and a moving force. 

We may remark at this point that modern physics is in some 
way extremely near to the doctrines of Heraclitus. If we replace 
the word 'fire' by the word 'energy' we can almost repeat his 
statements word for word from our modern point of view. 
Energy is in fact the substance from which all elementary par- 
ticles, all atoms and therefore all things are made, and energy is 
that which moves. Energy is a substance, since its total amount 
does not change, and the elementary particles can actually be 
made from this substance as is seen in many experiments on the 
creation of elementary particles. Energy can be changed into 
motion, into heat, into light, and- into tension. Energy may be 
called the fundamental cause for all change in the world. But 
this comparison of Greek philosophy with the ideas of modern 
science will be discussed later. 

Greek philosophy returned for some time to the concept of 
the One in the teachings of Parmenides, who lived in Elea in the 
south of Italy. His most important contribution to Greek think- 
ing was, perhaps, that he introduced a purely logical argument 



into metaphysics. 'One cannot know what is not — that is im- 
possible—nor utter it; for it is the same thing that can be thought! 
and that can be.' Therefore, only the One is, and there'is noj 
becoming or passing away. Parmenides denied the existence ofl 
empty space for logical reasons. Since all change requires empty! 
space, as he assumed, he dismissed change as an illusion . I 

But philosophy could not rest for long on this paradox. Em-j 
pedocles, from the south coast of Sicily, changed for the first! 
time from monism to a kind of pluralism. To avoid the difficulty| 
that one primary substance cannot explain the variety of things 
and events, he assumed four basic elements, earth, water, ah 
and fire. The elements are mixed together and separated by the 
action of Love and Strife. Therefore, these latter two, which arc 
in many ways treated as corporeal like the other four elementsj 
are responsible for the imperishable change. Empedocles de-| 
cribes the formation of the world in the following picture: Firstj 
there is the infinite Sphere of the One, as in the philosophy oij 
Parmenides. But in the primary substance all the four 'rootsj 
are mixed together by Love. Then, when Love is passing out and 
Strife coming in, the elements are partially separated and par-j 
tially combined. After that the elements are completely sep 
arated and Love is outside the World. Finally, Love is bringing 
the elements together again and Strife is passing out, so that w< 
return to the original Sphere. 

This doctrine of Empedocles represents a very definite turning 
toward a more materialistic view in Greek philosophy. The foul 
elements' are not so much fundamental principle as real maj 
terial substances. Here for the first time the idea is expressed thafl 
the mixture and separation of a few substances, which are fundaj 
mentally different, explains the infinite variety of things and 1 
events. Pluralism never appeals to those who are wont to thinl 
in fundamental principles. But it is a reasonable kind of comprc 
mise, which avoids the difficulty of monism and allows the estat 
lishment of some order. 

The next step toward the concept of the atom was made by 
Anaxagoras, who was a contemporary of Empedocles. He livec 
in Athens about thirty years, probably in the first half of the 
fifth century B.C. Anaxagoras stresses the idea of the mixturej 
the assumption that all change is caused by mixture and separa^ 


don. He assumes an infinite variety of infinitely small 'seeds' of 
which all things are composed. The seeds do not refer to the four 
elements of Empedocles, there are innumerably many different 
seeds. But the seeds are mixed together and separated again and 
in this way all change is brought about. The doctrine of Anaxag- 
oras allows for the first time a geometrical interpretation of the 
term 'mixture': Since he speaks of the infinitely small seeds, 
their mixture can be pictured as the mixture between two kinds 
of sand of different colours. The seeds may change in number 
and in relative position. Anaxagoras assumes that all seeds are in 
everything, only the proportion may change from one thing to 
another. He says: 'All things will be in everything; nor is it 
possible for them to be apart, but all things have a portion of 
everything.' The universe of Anaxagoras is set in motion not by 
Love and Strife, like that of Empedocles, but by 'Nous', which 
we may translate as 'Mind'. 

From this philosophy it was only one step to the concept of the 
atom, and this step occurred with Leucippus and Democritus of 
Abdera. The antithesis of Being and Not-being in the philosophy 
of Parmenides is here secularized into the antithesis of the 'Full' 
and the 'Void'. Being is not only One, it can be repeated an 
infinite number of times. This is the atom, the indivisible smallest 
unit of matter. The atom is eternal and indestructible, but it 
has a finite size. Motion is made possible through the empty 
space between the atoms. Thus for the first time in history there 
was voiced the idea of the existence of smallest ultimate par- 
ticles — we would say of elementary particles, as the fundamental 
building blocks of matter. 

According to this new concept of the atom, matter did not con- 
sist only of the 'Full', but also of the 'Void', of the empty space 
in which the atoms move. The logical objection of Parmenides 
against the Void, that not-being cannot exist, was simply ignored 
to comply with experience. From our modern point of view we 
would say that the empty space between the atoms in the philo- 
sophy of Democritus was not nothing; it was the carrier for 
geometry and kinematics, making possible the various arrange- 
ments and movements of atoms. But the possibility of empty 
space has always been a controversial problem in philosophy. 
In the theory of general relativity the answer is given that 

6 4 


geometry is produced by matter or matter by geometry, 
answer corresponds more closely to the view held by mar 
philosophers that space is defined by the extension of mattei 
But Democritus clearly departs from this view, to make chanf 
and motion possible. 

The atoms of Democritus were all of the same substanc 
which had the property of being, but had different sizes ar 
different shapes. They were pictured therefore as divisible in j 
mathematical but not in a physical sense. The atoms could moV 
and could occupy different positions in space. But they had li 
other physical properties. They had neither color nor smell n<j 
taste. The properties of matter which we perceive by our sens* 
were supposed to be produced by the movements and positiot 
of the atoms in space. Just as both tragedy and comedy can I 
written by using the same letters of the alphabet, the vast vanet 
of events in this world can be realized by the same atoms throu? 
their different arrangements and movements. Geometry ai 
kinematics, which were made possible by the void, proved to J 
still more important in some way than pure being. Democnt 
is quoted to have said : 'A thing merely appears to have colov 
it merely appears to be sweet or bitter. Only atoms and emptj 
space have a real existence . ' ^ 

The atoms in the philosophy of Leucippus do not move merej 
by chance. Leucippus seems to have believed in comply 
determinism, since he is known to have said: 'Naught happei 
for nothing, but everything from a ground and of necessity.' Tli 
atomists did not give any reason for the original motion of rt 
atoms, which just shows that they thought of a causal descnj 
tion of the atomic motion; causality can only explain later even! 
by earlier events, but it can never explain the beginning. 1 

The basic ideas of atomic theory were taken over and mo d| 
fied, in pait, by later Greek philosophers. For the sake of coiT 
parison with modern atomic physics it is important to mentic 
the explanation of matter given by Plato in his dialogi 
Timaeus. Plato was not an atomist; on the contrary, Diogend 
Laertius reported that Plato disliked Democritus so much thi 
he wished all his books to be burned. But Plato combined idesl 
that were near to atomism with the doctrines of the Pythagorea 
school and the teachings of Empedocles. 


The Pythagorean school was an offshoot of Orphism, which 
oes back to the worship of Dionysus. Here has been established 
the connection between religion and mathematics which ever 
since has exerted the strongest influence on human thought. The 
Pythagoreans seem to have been the first to realize the creative 
force inherent in mathematical formulations. Their discovery 
that two strings sound in harmony if their lengths are in a simple 
ratio demonstrated how much mathematics can mean for the 
understanding of natural phenomena. For the Pythagoreans it 
was not so much a question of understanding. For them the 
simple mathematical ratio between the length of the strings 
created the harmony in sound. There was also much mysticism 
in the doctrines of the Pythagorean school which for us is difficult 
to understand. But by making mathematics a part of their 
religion they touched an essential point in the development of 
human thought. I may quote a statement by Bertrand Russell 
about Pythagoras: 'I do not know of any other man who has been 
as influential as he was in the sphere of thought.' 

Plato knew of the discovery of the regular solids made by the 
Pythagoreans and of the possibility of combining them with the 
elements of Empedocles. He compared the smallest parts of the 
element earth with the cube, of air with the octahedron, of fire 
with the tetrahedron, and of water with the icosahedron. There 
is no element that corresponds to the dodecahedron; here Plato 
only says 'there was yet a fifth combination which God used in 
the delineation of the universe'. 

If the regular solids, which represent the four elements, can 
be compared with the atoms at all, it is made clear by Plato that 
they are not indivisible. Plato constructs the regular solids from 
two basic triangles, the equilateral and the isosceles triangles, 
which are put together to form the surface of the solids. There- 
fore, the elements can (at least partly) be transformed into each 
other. The regular solids can be taken apart into their triangles 
and new regular solids can be formed of them. For instance, 
one tetrahedron and two octahedra can be taken apart into 
twenty equilateral triangles, which can be recombined to give 
°ne icosahedron. That means: one atom of fire and two atoms 
of air can be combined to give one atom of water. But the funda- 
mental triangles cannot be considered as matter, since they have 



no extension in space. It is only when the triangles are puj 
together to form a regular solid that a unit of matter is created 
The smallest parts of matter are not the fundamental Beings, a 
in the philosophy of Democritus, but are mathematical forms 
Here it is quite evident that the form is more important than thd 
substance of which it is the form. 

After this short survey of Greek philosophy up to the formal 
tion of the concept of the atom we may come back to moderr^ 
physics and ask how our modern views on the atom and 01 
quantum theory compare with this ancient development. His 
torically the word 'atom' in modern physics and chemistry wa 
referred to the wrong object, during the revival of science in th« 
seventeenth century, since the smallest particles belonging t(j 
what is called a chemical element are still rather complicated 
systems of smaller units. These smaller units are nowadays called 
elementary particles, and it is obvious that if anything in moder 
physics should be compared with the atoms of Democritus 
should be the elementary particles like proton, neutron, electror 

Democritus was well aware of the fact that if the ator. 
should, by their motion and arrangements, explain the propertk 
of matter— colour, smell, taste— they cannot themselves hayj 
these properties. Therefore, he has deprived the atom of thesl 
qualities and his atom is thus a rather abstract piece of mattei 
But Democritus has left to the atom the quality of 'being', c 
extension in space, of shape and motion. He has left thes 
qualities because it would have been difficult to speak about thj 
atom at all if such qualities had been taken away from it? 
On the other hand, this implies that his concept of the ator 
cannot explain geometry, extension in space or existence, tw 
cause it cannot reduce them to something more fundamental 
The modern-view of the elementary particle with regard to thj 
point seems more consistent and more radical. Let us discuss tbf 
question: What is an elementary particle? We say, for instance 
simply 'a neutron' but we can give no well-defined picture anj 
what we mean by the word. We can use several pictures anj 
describe it once as a particle, once as a wave or as a wave packed 
But we know that none of these descriptions is accurate. Ceil 
tainly the neutron has no colour, no smell, no taste. In thii 


respect it resembles the atom of Greek philosophy. But even the 
other qualities are taken from the elementary particle, at least to 
some extent; the concepts of geometry and kinematics, like shape 
or motion in space, cannot be applied to it consistently. If one 
wants to give an accurate description of the elementary particle 
__ a nd here the emphasis is on the word 'accurate' — the only 
thing which can be written down as description is a probability 
function. But then one sees that not even the quality of being 
(if that may be called a 'quality') belongs to what is described. 
It is a possibility for being or a tendency for being. Therefore, 
the elementary particle of modern physics is still far more ab- 
stract than the atom of the Greeks, and it is by this very property 
more consistent as a clue for explaining the behaviour of matter. 

In the philosophy of Democritus all atoms consist of the same 
substance if the word 'substance' is to be applied here at all. 
The elementary particles in modern physics carry a mass in the 
same limited sense in which they have other properties. Since 
mass and energy are, according to the theory of relativity, essen- 
tially the same concepts, we may say that all elementary particles 
consist of energy. This could be interpreted as defining energy as 
the primary substance of the world. It has indeed the essential 
property belonging to the term 'substance', that it is conserved. 
Therefore, it has been mentioned before that the views of 
modern physics are in this respect very close to those of Hera- 
clitus if one interprets his element fire as meaning energy. 
Energy is in fact that which moves; it may be called the primary 
cause of all change, and energy can be transformed into matter 
or heat or light. The strife between opposites in the philosophy 
of Heraclitus can be found in the strife between two different 
forms of energy. 

In the philosophy of Democritus the atoms are eternal and 
^destructible units of matter, they can never be transformed 
into each other. With regard to this question modern physics 
takes a definite stand against the materialism of Democritus and 
or Plato and the Pythagoreans. The elementary particles are 
Ce rtainly not eternal and indestructible units of matter, they 
c ^n actually be transformed into each other. As a matter of fact, 
jt two such particles, moving through space with a very high 
!netic energy, collide, then many new elementary particles may 



be created from the available energy and the old particles 
may have disappeared in the collision. Such events have been 
frequently observed and offer the best proof that all particles are 
made of the same substance: energy. But the resemblance of thel 
modern views to those of Plato and the Pythagoreans can be! 
carried somewhat further. The elementary particles m Plato s 
Timaeus are finally not substance but mathematical forms. All 
things are numbers' is a sentence attributed to Pythagoras. Thel 
only mathematical forms available at that time were suchl 
geometric forms as the regular solids or the triangles which forml 
their surface. In modern quantum theory there can be no doubtl 
that the elementary particles will finally also be mathematical! 
forms, but of a much more complicated nature. The Greekl 
philosophers thought of static forms and found them m thel 
regular solids. Modern science, however, has from its beginning 
in the sixteenth and seventeenth centuries started from the 
dynamic problem. The constant element in physics since Newton 
is not a configuration or a geometrical form, but a dynamic lawj 
The equation of motion holds at all times, it is in this sense) 
eternal, whereas the geometrical forms, like the orbits are 
changing. Therefore, the mathematical forms that represent the 
elementary particles will be solutions of some eternal law ol 
motion for matter. Actually this is a problem which has nol 
yet been solved. The fundamental law of motion for matter Ti 
not yet known and therefore it is not yet possible to denyj 
mathematically the properties of the elementary particles frort 
such a law. But theoretical physics in its present state seems ti 
be not very far from this goal and we can at least say what kin< 
of law we have to expect. The final equation of motion fo* 
matter will probably be some quantized nonlinear wave equal 
tion for a wave field of operators that simply represents matterl 
not any specified kind of waves or particles. This wave equatioj 
will probably be equivalent to rather complicated sets of Integra 
equations, which have 'Eigenvalues' and 'Eigensolutions , al 
the physicists call it. These Eigensolutions will finally represenl 
the elementary particles; they are the mathematical forms whicl 
shall replace the regular solids of the Pythagoreans. We mighj 
mention here that these 'Eigensolutions' will follow from tbi 
fundamental equation for matter by much the same math© 


matical process by which the harmonic vibrations of the Pythag- 
orean string follow from the differential equation of the string. 
But, as has been said, these problems are not yet solved. 

If we follow the Pythagorean line of thought we may hope 
that the fundamental law of motion will turn out as a mathe- 
matically simple law, even if its evaluation with respect to the 
Eigenstates may be very complicated. It is difficult to give any 
good argument for this hope for simplicity — except the fact that 
it has hitherto always been possible to write the fundamental 
equations in physics in simple mathematical forms. This fact 
fits in with the Pythagorean religion, and many physicists share 
their belief in this respect, but no convincing argument has yet 
been given to show that it must be so. 

We may add an argument at this point concerning a question 
which is frequently asked by laymen with respect to the concept 
of the elementary particle in modern physics: Why do the 
physicists claim that their elementary particles cannot be divided 
into smaller bits? The answer to this question clearly shows 
how much more abstract modern science is as compared to 
Greek philosophy. The argument runs like this: How could one 
divide an elementary particle? Certainly only by using extreme 
forces and very sharp tools. The only tools available are other 
elementary particles. Therefore, collisions between two ele- 
mentary particles of extremely high energy would be the only 
processes by which the particles could eventually be divided. 
Actually they can be divided in such processes, sometimes into 
very many fragments; but the fragments are again elementary 
particles, not any smaller pieces of them, the masses of these 
fragments resulting from the very large kinetic energy of the 
two colliding particles. In other words, the transmutation of 
energy into matter makes it possible that the fragments of ele- 
mentary particles are again the same elementary particles. 

After this comparison of the modern views in atomic physics 
with Greek philosophy we have to add a warning, that this 
comparison should not be misunderstood. It may seem at first 
sight that the Greek philosophers have by some kind of in- 
genious intuition come to the same or very similar conclusions 
as we have in modern times only after several centuries of hard 
labour with experiments and mathematics. This interpretation 



of our comparison would, however, be a complete misunder- 
standing. There is an enormous difference between modern 
science and Greek philosophy, and that is just the empinstic 
attitude of modern science. Since the time of Galileo and New- 
ton, modern science has been based upon a detailed study of 
nature and upon the postulate that only such statements should 
be made, as have been verified or at least can be verified by 
experiment. The idea that one could single out some events from 
nature by an experiment, in order to study the details and to 
find out what is the constant law in the continuous change, did 
not occur to the Greek philosophers. Therefore, modern science 
has from its beginning stood upon a much more modest, but at 
the same time much firmer, basis than ancient philosophy. 
Therefore, the statements of modern physics are in some way 
meant much more seriously than the statements of Greek phi- 
losophy. When Plato says, for instance, that the smallest particles 
of fire are tetrahedrons, it is not quite easy to see what he really 
means. Is the form of the tetrahedron only symbolically attached 
to the element fire, or do the smallest particles of fire mechani- 
cally act as rigid tetrahedrons or as elastic tetrahedrons, and by 
what force could they be separated into the equilateral triangles, 
etc ■> Modern science would finally always ask: How can one 
decide experimentally that the atoms of fire are tetrahedrons 
and not perhaps cubes? Therefore, when modern science states 
that the proton is a certain solution of a fundamental equation of 
matter it means that we can from this solution deduce mathe- 
matically all possible properties of the proton and can check the 
correctness of the solution by experiments in every detail. This 
possibility of checking the correctness of a statement experi- 
mentally with very high precision and in any number of detads 
gives an enormous weight to the statement that could not be 
attached to the statements of early Greek philosophy. 

All the same, some statements of ancient philosophy are rather 
near to those of modern science. This simply shows how far one 
can get by combining the ordinary experience of nature that we 
have without doing experiments with the untiring effort to get 
some logical order into this experience to understand it from 
general principles. 

The Development of Philosophical Ideas 

Since Descartes in Comparison with the 

New Situation in Quantum Theory 

IN THE two thousand years that followed the culmination of 
Greek science and culture in the fifth and fourth centuries B.C. 
the human mind was to a large extent occupied with problems 
of a different kind from those of the early period. In the first 
centuries of Greek culture the strongest impulse had come from 
the immediate reality of the world in which we live and which 
we perceive by our senses. This reality was full of life and there 
was no good reason to stress the distinction between matter and 
mind or between body and soul. But in the philosophy of Plato 
one already sees that another reality begins to become stronger. 
In the famous simile of the cave Plato compares men to prisoners 
in a cave who are bound and can look in only one direction. 
They have a fire behind them and see on a wall the shadows of 
themselves and of objects behind them. Since they see nothing 
but the shadows, they regard those shadows as real and are not 
aware of the objects. Finally one of the prisoners escapes and 
comes from the cave into the light of the sun. For the first time 
he sees real things and realizes that he had been deceived 
hitherto by the shadows. For the first time he knows the truth 
and thinks only with sorrow of his long life in the darkness. The 
real philosopher is the prisoner who has escaped from the cave 
into the light of truth, he is the one who possesses real knowl- 
edge. This immediate connection with truth or, we may in the 
Christian sense say, with God is the new reality that has begun 
to become stronger than the reality of the world as perceived by 

7 2 


our senses. The immediate connection with God happens within 
the human soul, not in the world, and this was the problem that 
occupied human thought more than anything else in the two 
thousand years following Plato. In this period the eyes of the 
philosophers were directed toward the human soul and its rela- 
tion to God, to the problems of ethics, and to the interpretation 
of the revelation but not to the outer world. It was only in the 
time of the Italian Renaissance that again a gradual change of 
the human mind could be seen, which resulted finally in a re- 
vival of the interest in nature. 

The great development of natural science since the sixteenth 
and seventeenth centuries was preceded and accompanied by a 
development of philosophical ideas which were closely con- 
nected with the fundamental concepts of science. It may there- 
fore be instructive to comment on these ideas from the position j 
that has finally been reached by modern science in our time. j 

The first great philosopher of this new period of science was 
Rend Descartes who lived in the first half of the seventeenth 
century. Those of his ideas that are most important for the 
development of scientific thinking are contained in his Discourse! 
on Method. On the basis of doubt and logical reasoning he tries! 
to find a completely new and as he thinks solid ground for al 
philosophical system. He does not accept revelation as such al 
basis nor does he want to accept uncritically what is perceived! 
by the senses. So he starts with his method of doubt. He casts! 
his doubt upon that which our senses tell us about the results off 
our reasoning and finally he arrives at his famous sentence 
'cogito ergo sum'. I cannot doubt my existence since it followsj 
from the fact that I am thinking. After establishing the existence 
of the I in this way he proceeds to prove the existence of Gc 
essentially on the lines of scholastic philosophy. Finally the exi; 
ence of the world follows from the fact that God had given me 
a strong inclination to believe in the existence of the world, and 
it is simply impossible that God should have deceived me. 

This basis of the philosophy of Descartes is radically different 
from that of the ancient Greek philosophers. Here the starting 
point is not a fundamental principle or substance, but the at 
tempt of a fundamental knowledge. And Descartes realizes 
that what we know about our mind is more certain than what we 


know about the outer world. But already his starting point with 
t he triangle' God - World I simplifies in a dangerous way the 
basis for further reasoning. The division between matter and 
mind or between soul and body, which had started in Plato's 
philosophy, is now complete. God is separated both from the I 
and from the world. God in fact is raised so high above the world 
and men that He finally appears in the philosophy of Descartes 
only as a common point of reference that establishes the relation 
between the I and the world. 

While ancient Greek philosophy had tried to find order in the 
infinite variety of things and events by looking for some funda- 
mental unifying principle, Descartes tries to establish the order 
through some fundamental division. But the three parts which 
result from the division lose some of their essence when any one 
part is considered as separated from the other two parts. If one 
uses the fundamental concepts of Descartes at all, it is essential 
that God is in the world and in the I and it is also essential that 
the I cannot be really separated from the world. Of course 
Descartes knew the undisputable necessity of the connection, but 
philosophy and natural science in the following period developed 
on the basis of the polarity between the 'res cogitans' and the 
'res extensa', and natural science concentrated its interest on 
the 'res extensa'. The influence of the Cartesian division on 
human thought in the following centuries can hardly be over- 
estimated, but it is just this division which we have to criticize 
later from the development of physics in our time. 

Of course it would be wrong to say that Descartes, through 
his new method in philosophy, has given a new direction to 
human thought. What he actually did was to formulate for the 
first time a trend in human thinking that could already be seen 
during the Renaissance in Italy and in the Reformation. There 
was the revival of interest in mathematics which expressed an 
increasing influence of Platonic elements in philosophy, and the 
msistence on personal religion. The growing interest in mathe- 
matics favoured a philosophical system that started from logical 
reasoning and tried by this method to arrive at some truth that 
Was as certain as a mathematical conclusion. The insistence on 
Personal religion separated the I and its relation to God from the 
w orld. The interest in the combination of empirical knowledge 



with mathematics as seen in the work of Galileo was perhaps 
partly due to the possibility of arriving in this way at some 
knowledge that could be kept apart completely from the theo- 
logical disputes raised by the Reformation. This empirica^ 
knowledge could be formulated without speaking about God oi 
about ourselves and favoured the separation of the three f undaj 
mental concepts God-World-I or the separation between 'res 1 
ccgitans' and 'res extensa'. In this period there was in some 
cases an explicit agreement among the pioneers of empirical 
science that in their discussions the name of God or a fundaj 
mental cause should not be mentioned. 

On the other hand, the difficulties of the separation could 
clearly seen from the beginning. In the distinction, for instance! 
between the 'res cogitans' and the 'res extensa' Descartes wad 
forced to put the animals entirely on the side of the 'res exl 
tensa'. Therefore, the animals and the plants were not essert 
tially different from machines, their behaviour was completely 
determined by material causes. But it has always seemed difficul^ 
to deny completely the existence of some kind of soul in the ani 
mals, and it seems to us that the older concept of soul for instana 
in the philosophy of Thomas Aquinas was more natural and 
less forced than the Cartesian concept of the 'es cognitans'j 
even if we are convinced that the laws of physics and chemistr 
are strictly valid in living organisms. One of the later cons 
quences of this view of Descartes was that, if animals wer 
simply considered as machines, it was difficult not to think the 
same about men. Since, on the other hand, the 'res cogitans] 
and the 'res extensa' were taken as completely different in theij 
essence, it did not seem possible that they could act upon eac 
other. Therefore, in order to preserve complete parallelism b 
tween the experiences of the mind and of the body, the mind als 
was in its activities completely determined by laws which corre 
sponded to the laws of physics and chemistry. Here the questioi 
of the possibility of 'free will* arose. Obviously this whole de 
scription is somewhat artificial and shows the grave defects o^ 
the Cartesian partition. j 

On the other hand in natural science the partition was foj 
several centuries extremely successful. The mechanics of Newtoi) 
and all the other parts of classical physics constructed after it' 


n iodel started from the assumption that one can describe the 
w orld without speaking about God or ourselves. This possibility 
soon seemed almost a necessary condition for natural science in 

But at this point the situation changed to some extent through 
quantum theory and therefore we may now come to a com- 
parison of Descartes's philosophical system with our present 
situation in modern physics. It has been pointed out before that 
in the Copenhagen interpretation of quantum theory we can 
indeed proceed without mentioning ourselves as individuals, but 
we cannot disregard the fact that natural science is formed by 
men. Natural science does not simply describe and explain 
nature; it is a part of the interplay between nature and our- 
selves; it describes nature as exposed to our method of question- 
ing. This was a possibility of which Descartes could not have 
thought, but it makes the sharp separation between the world 
and the I impossible. 

If one follows the great difficulty which even eminent 
scientists like Einstein had in understanding and accepting the 
Copenhagen interpretation of quantum theory, one can trace the 
roots of this difficulty to the Cartesian partition. This partition 
has penetrated deeply into the human mind during the three 
centuries following Descartes and it will take a long time for it to 
be replaced by a really different attitude toward the problem of 

The position to which the Cartesian_partition has led with 
respect to the 'res extensa' was what one may call metaphysical 
realism. The world, i.e., the extended things, 'exist'. This is to 
he distinguished from practical realism, and the different forms 
°f realism may be described as follows: We 'objectivate' a 
statement if we claim that its content does not depend on the 
conditions under which it can be verified. Practical realism as- 
sumes that there are statements that can be objectivated and 
Aat in fact the largest part of our experience in daily life consists 
°f such statements. Dogmatic realism claims that there are no 
Statements concerning the material world that cannot be ob- 
l e ctivated. Practical realism has always been and will always be 
an essential part of natural science. Dogmatic realism, however, 
ls . as we see it now, not a necessary condition for natural science. 



But it has in the past played a very important role in the de 
velopment of science; actually the position of classical physics i 
that of dogmatic realism. It is only through quantum theory tha 
we have learned that exact science is possible without the basi 
of dogmatic realism. When Einstein has criticized quantur 
theory he has done so from the basis of dogmatic realism. lh 
is a very natural attitude. Every scientist who does research worl 
feels that he is looking for something that is objectively true. H* 
statements are not meant to depend upon the conditions unde 
which they can be verified. Especially in physics the fact that wl 
can explain nature by simple mathematical laws tells us thai 
here we have met some genuine feature of reality, not something 
that we have-in any meaning of the word-invented ourse ved 
This is the situation which Einstein had in mind when he tool 
dogmatic realism as the basis for natural science. But quanturt 
theory is in itself an example for the possibility of explaimnl 
nature by means of simple mathematical laws without this basij 
These laws may perhaps not seem quite simple when one com- 
pares them with Newtonian mechanics. But, judging from t» 
enormous complexity of the phenomena which are to be cj 
plained (for instance, the line spectra of complicated atoms) 
the mathematical scheme of quantum theory is comparativeW 
simple. Natural science is actually possible without the basis d 
dogmatic realism. 

Metaphysical realism goes one step further than dogmat 
realism by saying that 'the things really exist'. This is in tac 
what Descartes tried to prove by the argument that God cannc 
have deceived us.' The statement that the things really exist 
different from the statement of dogmatic realism in so far i 
here the word 'exist' occurs, which is also meant in the othe 
statement 'cogito ergo sum' . . . T think, therefore I am. Bi 
it is difficult to see what is meant at this point that is not ye 
contained in the thesis of dogmatic realism; and this leads u 
to a general cricism of the statement 'cogito ergo sum whicl 
Descartes considered as the solid ground on which he coull 
build his system. It is in fact true that this statement has tM 
certainty of a mathematical conclusion, if the words cogito 
and 'sum' are defined in the usual way or, to put it mof 
cautiously and at the same time more critically, if the words ar 


so defined that the statement follows. But this does not tell us 
anything about how far we can use the concepts of 'thinking' 
and 'being' in finding our way. It is finally in a very general 
sense always an empirical question how far our concepts can be 

The difficulty of metaphysical realism was felt soon after 
Descartes and became the starting point for the empiristic 
philosophy, for sensualism and positivism. 

The three philosophers who can be taken as representatives 
for early empiristic philosophy are Locke, Berkeley and Hume. 
Locke holds, contrary to Descartes, that all knowledge is ulti- 
mately founded in experience. This experience may be sensation 
or perception of the operation of our own mind. Knowledge, so 
Locke states, is the perception of the agreement or disagreement 
of two ideas. The next step was taken by Berkeley. If actually all 
our knowledge is derived from perception, there is no meaning 
in the statement that the things really exist; because if the per- 
ception is given it cannot possibly make any difference whether 
the things exist or do not exist. Therefore, to be perceived is 
identical with existence. This line of argument then was ex- 
tended to an extreme skepticism by Hume, who denied induc- 
tion and causation and thereby arrived at a conclusion which 
if taken seriously would destroy the basis of all empirical science. 

The criticism of metaphysical realism which has been ex- 
pressed in empiristic philosophy is certainly justified in so far as 
it is a warning against the naive use of the term 'existence'. The 
positive statements of this philosophy can be criticized on similar 
lines. Our perceptions are not primarily bundles of colours or 
sounds; what we perceive is already perceived as something, the 
accent here being on the word 'thing', and therefore it is doubt- 
ful whether we gain anything by taking the perceptions instead 
of the things as the ultimate elements of reality. 

The underlying difficulty has been clearly recognized by 
modern positivism. This line of thought expresses criticism 
against the naive use of certain terms like 'thing', 'perception', 
existence' by the general postulate that the question whether 
a given sentence has any meaning at all should always be 
thoroughly and critically examined. This postulate and its under- 
lying attitude are derived from mathematical logic. The pro- 


cedure of natural science is pictured as an attachment of symbols 
to the phenomena. The symbols can, as in mathematics, be com- 
bined according to certain rules, and in this way statements \ 
about the phenomena can be represented by combinations of 
symbols. However, a combination of symbols that does not com- 
ply with the rules is not wrong but conveys no meaning. 

The obvious difficulty in this argument is the lack of any 
general criterion as to when a sentence should be considered as 
meaningless. A definite decision is possible only when the sen- 
tence belongs to a closed system of concepts and axioms, which 
in the development of natural science will be rather the exception 
than the rule. In some cases the conjecture that a certain sen- 
tence is meaningless has historically led to important progress, 
for it opened the way to the establishment of new connections 
which would have been impossible if the sentence had a mean- 
ing. An example in quantum theory that has already been dis- 
cussed is the sentence: 'In which orbit does the electron move 
around the nucleus?'' But generally the positivistic scheme taken 
from mathematical logic is too narrow in a description of nature 
which necessarily uses words and concepts that are only vaguely 

The philosophic thesis that all knowledge is ultimately 
founded in experience has in the end led to a postulate concern- 
ing the logical clarification of any statement about nature. Such 
a postulate may have seemed justified in the period of classical 
physics, but since quantum theory we have learned that it cannot 
be fulfilled. The words 'position' and 'velocity' of an electron, 
for instance, seemed perfectly well defined as to both their 
meaning and their possible connections, and in fact they were 
clearly defined concepts within the mathematical framework of 
Newtonian mechanics. But actually they were not well defined, 
as is seen from the relations of uncertainty. One may say that 
regarding their position in Newtonian mechanics they were well 
defined, but in their relation to nature they were not. This shows 
that we can never know beforehand which limitations will be 
put on the applicability of certain concepts by the extension 
of our knowledge into the remote parts of nature, into which we 
can only penetrate with the most elaborate tools. Therefore, in 
the process of penetration we are bound sometimes to use our 


concepts in a way which is not justified and which carries no 
meaning. Insistence on the postulate of complete logical clari- 
fication would make science impossible. We are reminded here 
by modern physics of the old wisdom that the one who insists on 
never uttering an error must remain silent. 

A combination of those two lines of thought that started from 
Descartes, on the one side, and from Locke and Berkeley, on the 
other, was attempted in the philosophy of Kant, who was the 
founder of German idealism. That part of his work which is im- 
portant in comparison with the results of modern physics is 
contained in The Critique of Ture Reason. He takes up the 
question whether knowledge is only founded in experience or 
can come from other sources, and he arrives at the conclusion 
that our knowledge is in part 'a priori' and not inferred induc- 
tively from experience. Therefore, he distinguishes between 
'empirical' knowledge and knowledge that is 'a priori'. At the 
same time he distinguishes between 'analytic' and 'synthetic' 
propositions'. Analytic propositions follow simply from logic, and 
their denial would lead to self-contradiction. Propositions that 
arejiaL!analytic' are called 'synthetic'. 

What is, according to Kant, the criterion for knowledge being 
'a priori'? Kant agrees that all knowledge starts with experience 
but he adds that it is not always derived from experience. It is 
true that experience teaches us that a certain thing has such or 
such properties, but it does not teach us that it could not be 
different. Therefore, if a proposition is thought together with its 
necessity it must be 'a priori'. Experience never gives to its 
judgments complete generality. For instance, the sentence 'The 
sun rises every morning' means that we know no exception to 
this rule in the past and that we expect it to hold in future. But 
we can imagine exceptions to the rule. If a judgment is stated 
with complete generality, therefore, if it is impossible to imagine 
any exception, it must be 'a priori'. An analytic judgment is 
always 'a priori'; even if a child learns arithmetic from playing 
with marbles, he need not later go back to experience to know 
that 'two and two are four'. Empirical knowledge, on the other 
hand, is synthetic. 

But are synthetic judgments a priori possible? Kant tries to 
prove this by giving examples in which the above criteria seem 


to be fulfilled. Space and time are, he says, a priori forms of pure! 
intuition. In the case of space he gives the following meta-j 

physical arguments: 

i Space is not an empirical concept, abstracted from other 

experiences, for space is presupposed in referring sensations tol 
something external, and external experience is only possible] 
through the presentation of space. 1 

2 Space is a necessary presentation a prion, which underlies all] 
external perceptions; for we cannot imagine that there should be] 
no space, although we can imagine that there should be nothing! 

in space. . . 1 

7 Space is not a discursive or general concept of the relations! 
of things in general, for there is only one space, of which what! 
we call'spaces' are parts, not instances. 1 

4 Space is presented as an infinite given magnitude, whichj 
holds within itself all the parts of space; this relation is different] 
from that of a concept to its instances, and therefore space is noti 
a concept but a form of intuition. 

These arguments shall not be discussed here. They are men- 
tioned merely as examples for the general type of proof that! 
Kant has in mind for the synthetic judgments a priori. 

With regard to physics Kant took as a priori, besides space 
and time the law of causality and the concept of substance. In] 
a later stage of his work he tried to include the law of consent 
tion of matter, the equality of 'actio and reactio' and even the 
law of gravitation. No physicist would be willing to follow Kant] 
here if the term 'a priori' is used in the absolute sense that was] 
given to it by Kant. In mathematics Kant took Euclidean] 
geometry as 'a priori'. 

Before we compare these doctrines of Kant with the results of 
modern physics we must mention another part of his work, to 
which we will have to refer later. The disagreeable question 
whether 'the things really exist', which had given rise to em-f 
piristic philosophy, occurred also in Kant's system. But Kant 
has not followed the line of Berkeley and Hume, though that 
would have been logically consistent. He kept the notion of the 
'thing-in-itself as different from the percept, and in this way 
kept some connection with realism. 
Coming now to the comparison of Kant's doctrines with] 


modern physics, it looks in the first moment as though his central 
concept of the 'synthetic judgments a priori' had been com- 
pletely annihilated by the discoveries of our century. The theory 
f relativity has changed our views on space and time, it has in 
fact revealed entirely new features of space and time, of which 
nothing is seen in Kant's a priori forms of pure intuition. The 
law of causality is no longer applied in quantum theory and the 
law of conservation of matter is no longer true for the ele- 
mentary particles. Obviously Kant could not have foreseen the 
new discoveries, but since he was convinced that his concepts 
would be 'the basis of any future metaphysics that can be called 
science' it is interesting to see where his arguments have been 

As example we take the law of causality. Kant says that when- 
ever we observe an event we assume that there is a foregoing 
event from which the other event must follow according to some 
rule. This is, as Kant states, the basis of all scientific work. In 
this discussion it is not important whether or not we can always 
find the foregoing event from which the other one followed. 
Actually we can find it in many cases. But even if we cannot, 
nothing can prevent us from asking what this foregoing event 
might have been and to look for it. Therefore, the law of cau- 
sality is reduced to the method of scientific research; it is the 
condition which makes science possible. Since we actually apply 
this method, the law of causality is 'a priori' and is not derived 
from experience. 

Is thjsjrue^atomic^hysics? Let us consider a radium atom, 
which can emit an a-particle. The time for the emission of the 
a-particle cannot be predicted. We can only say that in the 
average the emission will take place in about two thousand years. 
Therefore, when we observe the emission we do not actually look 
for a foregoing event from which the emission must according, 
to a rule follow. Logically it would be quite possible toiook for 
such a foregoing event, and we need not be discouraged by the 
fact that hitherto none has been found. But why has the scien- 
tific method actually changed in this very fundamental question 
since Kant? 

Two possible answers can be given to that question. The one 
1S: We have been convinced by experience that the laws of 



quantum theory are correct and, if they are, we know that 
foregoing event as cause for the emission at a given time cannot 
be found. The other answer is: We know the foregoing event! 
but not quite accurately. We know the forces in the atomi<| 
nucleus that are responsible for the emission of the a-particlej 
But this knowledge contains the uncertainty which is brought 
about by the interaction between the nucleus and the rest of thd 
world. If we wanted to know why the a-particle was emitted afl 
that particular time we would have to know the microscopid 
structure of the whole world including ourselves, and that is iml 
possible. Therefore, Kant's arguments for the a priori charactef 
of the law of causality no longer apply. 

A similar discussion could be given on the a priori characte 
of space and time as forms of intuition. The result would be thd 
same. The a priori concepts which Kant considered an undisj 
putable truth are no longer contained in the scientific system o< 
modern physics. ] 

Still they form an essential part of this system in a somewhal 
different sense. In the discussion of the Copenhagen interpretaj 
tion of quantum theory it has been emphasized that we use th| 
classical concepts in describing our experimental equipment an^ 
more generally in describing that part of the world which dc^ 
not belong to the object of the experiment. The use of the 
concepts, including space, time and causality, is in fact thd 
condition for observing atomic events and is, in this sense of thl 
word, 'a priori'. What Kant had not foreseen was that these J 
priori concepts can be the conditions for science and at the samj 
time can have only a limited range of applicability. When w 1 
make an experiment we have to assume a causal chain of event 
that leads from the atomic event through the apparatus nnallj 
to the eye of the observer; if this causal chain was not assumed 1 
nothing could be known about the atomic event. Still we mus 
keep in mind that classical physics and causality have only 
limited range of applicability. It was the fundamental parade 
of quantum theory that could not be foreseen by Kant. Moderj 
physics has changed Kant's statement about the possibility c 
synthetic judgments a priori from a metaphysical one into 
practical one. The synthetic judgments a priori thereby havi 
the character of a relative truth. 


If one reinterprets the Kantian 'a priori' in this way, there 
is no reason to consider the perceptions rather than the things as 
given. Just as in classical physics, we can speak about those 
events that are not observed in the same manner as about those 
that are observed. Therefore, practical realism is a natural part 
of the reinterpretation. Considering the Kantian 'thing-in-itself ' 
Kant had pointed out that we cannot conclude anything from 
the perception about the 'thing-in-itself. This statement has, as 
VVeizsacker has noticed, its formal analogy in the fact that in 
spite of the use of the classical concepts in all the experiments a 
nonclassical behaviour of the atomic objects is possible. The 
'thing-in-itself is for the atomic physicist, if he uses this con- 
cept at all, finally a mathematical structure; but this structure 
is — contrary to Kant — indirectly deduced from experience. 

In this reinterpretation the Kantian 'a priori' is indirectly 
connected with experience in so far as it has been formed 
through the development of the human mind in a very distant 
past. Following this argument the biologist Lorentz has once 
compared the 'a priori' concepts with forms of behaviour that in 
animals are called 'inherited or innate schemes'. It is in fact 
quite plausible that for certain primitive animals space and time 
are different from what Kant calls our 'pure intuition' of space 
and time. The latter may belong to the species 'man', but not 
to the world as independent of men. But we are perhaps entering 
into too hypothetical discussions by following this biological 
comment on the 'a priori'. It was mentioned here merely as an 
example of how the term 'relative truth' in connection with the 
Kantian 'a priori' can possibly be interpreted. 

Modern physics has been used here as an example or, we may 
say, as a model to check the results of some important philo- 
sophic systems of the past, which of course were meant to hold 
in a much wider field. What we have learned especially from 
the discussion of the philosophies of Descartes and Kant may 
perhaps be stated in the following way: 

Any concepts or words which have been formed in the past 
through the interplay between the world and ourselves are not 
really sharply denned with respect to their meaning; that is to 
say, we do not know exactly how far they will help us in finding 
our way in the world. We often know that they can be applied 


to a wide range of inner or outer experience, but we practically 
never know precisely the limits of their applicability. This is trul 
even of the simplest and most general concepts like 'existence 
and 'space and time'. Therefore, it will never be possible bjj 
pure reason to arrive at some absolute truth. 

The concepts may, however, be sharply defined with regar<j 
to their connections. This is actually the fact when the concept 
become a part of a system of axioms and definitions which ca| 
be expressed consistently by a mathematical scheme. Such 
group of connected concepts may be applicable to a wide field ol 
experience and will help us to find our way in this field. But th<| 
limits of the applicability will in general not be known, at leas<| 
not completely. 

Even if we realize that the meaning of a concept is never de 
fined with absolute precision, some concepts form an integra^ 
part of scientific methods, since they represent for the time being 
the final result of the development of human thought in the past! 
even in a very remote past; they may even be inherited and arfj 
in any case the indispensable tools for doing scientific work ii 
our time. In this sense they can be practically a priori. Bu^j 
further limitations of their applicability may be found in the 

The Relation of Quantum Theory to 
Other Parts of Natural Science 

IT HAS been stated before that the concepts of natural science 
can sometimes be sharply defined with regard to their connec- 
tions. This possibility was realized for the first time in Newton's 
Trincipia and it is just for that reason that Newton's work has 
exerted its enormous influence on the whole development of 
natural science in the following centuries. Newton begins his 
Trincipia with a group of definitions and axioms which are inter- 
connected in such a way that they form what one may call a 
'closed system'. Each concept can be represented by a mathe- 
matical symbol, and the connections between the different con- 
cepts are then represented by mathematical equations expressed 
by means of the symbols. The mathematical image of the system 
ensures that contradictions cannot occur in the system. In this 
way the possible motions of bodies under the influence of the 
acting forces are represented by the possible solutions of the 
equations. The system of definitions and axioms which can be 
written in a set of mathematical equations is considered as de- 
scribing an eternal structure of nature, depending neither on a 
particular space nor on particular time. 

The connection between the different concepts in the system 
is so close that one could generally not change any one of the 
concepts without destroying the whole system. 

For this reason Newton's system was for a long time con- 
sidered as final and the task set before the scientists of the fol- 
lowing period seemed simply to be an expansion of Newton's 
mechanics into wider fields of experience. Actually physics did 
develop along these lines for about two centuries. 



From the theory of the motion of mass points one could go ; 
over the mechanics of solid bodies, to rotatory motions, and) 
one could treat the continuous motions of a fluid or the vibrating i 
motions of an elastic body. All these parts of mechanics ot\ 
dynamics were gradually developed in close connection with the j 
evolution of mathematics, especially of the differential calculus, j 
and the results were checked by experiments. Acoustics andi 
hydrodynamics became a part of mechanics. Another science, in j 
which the application of Newton's mechanics was obvious, wasf 
astronomy. The improvements of the mathematical methods 
gradually led to more and more accurate determinations of the 
motions of the planets and of their mutual interactions. When] 
the phenomena of electricity and magnetism were discovered, 
the electric or magnetic forces were compared to the gravita- 
tional forces and their actions upon the motion of the bodies 
could again be studied along the lines of Newtonian mechanics.! 
Finally, in the nineteenth century, even the theory of heat could 
be reduced to mechanics by the assumption that heat really con- 
sists of a complicated statistical motion of the smallest parts of 1 
matter. By combining the concepts of the mathematical theory! 
of probability with the concepts, of Newtonian mechanics! 
Clausius Gibbs and Boltzmann were able to show that the! 
fundamental laws in the theory of heat could be interpreted asl 
statistical laws following from Newton's mechanics whenj 
applied to very complicated mechanical systems. 

Up to this point the programme set up by Newtonian mech-^ 
anics had been carried out quite consistently and had led to thel 
understanding of a wide field of experience. The first difficulty! 
arose in the discussions on the electromagnetic field in the worn 
of Faraday and Maxwell. In Newtonian mechanics the gravitaj 
tional force had been considered as given, not as an object foil 
further theoretical studies. In the work of Faraday and Max-1 
well, however, the field of force itself became the object of the! 
investigation; the physicists wanted to know how this field oil 
force varied as function of space and time. Therefore, they tried! 
to set up equations of motion for the fields, not primarily for thel 
bodies upon which the fields act. This change led back to al 
point of view which had been held by many scientists before! 
Newton. An action could, so it seemed, be transferred from one] 


body to another only when the two bodies touched each other; 
for instance, in a collision or through friction. Newton had intro- 
duced a very new and strange hypothesis by assuming a force 
that acted over a long distance. Now in the theory of the fields 
of force one could come back to the older idea, that action is 
transferred from one point to a neighbouring point, only by de- 
scribing the behaviour of the fields in terms of differential equa- 
tions. This proved actually to be possible, and therefore the 
description of the electromagnetic fields as given by Maxwell's 
equations seemed a satisfactory solution to the problem of force. 
Here one had really changed the programme given by New- 
tonian mechanics. The axioms and definitions of Newton had re- 
ferred to bodies and their motion; but with Maxwell the fields of 
force seemed to have acquired the same degree of reality as the 
bodies in Newton's theory. This view of course was not easily ac- 
cepted; and to avoid such a change in the concept of reality it 
seemed plausible to compare the electromagnetic fields with the 
fields of elastic deformation or stress, the light waves of Max- 
well's theory with the sound waves in elastic bodies. Therefore, 
many physicists believed that Maxwell's equations actually re- 
ferred to the deformations of an elastic medium, which they 
called the ether; and this name was given merely to explain that 
the medium was so light and thin that it could penetrate into 
other matter and could not be seen or felt. This explanation was 
not too satisfactory, however, since it could not explain the 
complete absence of any longitudinal light waves. 

Finally the theory of relativity, which will be discussed in the 
next chapter, showed in a conclusive way that the concept of the 
ether as a substance, to which Maxwell's equations refer, had to 
be abandoned. The arguments cannot be discussed at this point; 
but the result was that the fields had to be considered as an inde- 
pendent reality. 

A further and still more startling result of the theory of special 
relativity was the discovery of new properties of space and time, 
actually of a relation between space and time that had not been 
known before and did not exist in Newtonian mechanics. 

Under the impression of this completely new situation many 
physicists came to the following somewhat rash conclusion: 
Newtonian mechanics had finally been disproved. The primary 



reality is the field and not the body, and the structure of space 
and time is correctly described by the formulas of Lorentz and 
Einstein, and not by the axioms of Newton. The mechanics of 
Newton was a good approximation in many cases, but now it 
must be improved to give a more rigorous description of nature. 
From the point of view which we have finally reached in 
quantum theory such a statement would appear as a very poor 
description of the actual situation. First, it ignores the fact that 
most experiments by which fields are measured are based upon 
Newtonian mechanics and, second, that Newtonian mechanics 
cannot be improved; it can only be replaced by something essen- 
tially different! 

The development of quantum theory has taught us that one 
should rather describe the situation in the following terms: 
Wherever the concepts of Newtonian mechanics can be used to 
describe events in nature, the laws formulated by Newton are 
strictly correct and cannot be improved. But the electromagnetic 
phenomena cannot adequately be described by the concepts of 
Newtonian mechanics. Therefore, the experiments on the 
electromagnetic fields and on light waves, together with their 
theoretical analysis by Maxwell, Lorentz and Einstein, have led 
to a new closed system of definitions and axioms and of con- 
cepts that can be represented by mathematical symbols, which 
is coherent in the same sense as the system of Newton's me- 
chanics, but is essentially different from it. 

Therefore, even the hopes which had accompanied the work 
of the scientists since Newton had to be changed. Apparently 
progress in science could not always be achieved by using the 
known laws of nature for explaining new phenomena. In some 
cases new phenomena that had been observed could only be 
understood by new concepts which were adapted to the new 
phenomena in the same way as Newton's concepts were to the 
mechanical events. These new concepts again could be con- 
nected in a closed system and represented by mathematical 
symbols. But if physics or, more generally, natural science pro- 
ceeded in this way, the question arose: What is the relation be- 
tween the different sets of concepts? If, for instance, the same 
concepts or words occur in two different sets and are defined 
differently with regard to their connection and mathematical 


representation, in what sense do the concepts represent reality? 

This problem arose at once when the theory of special rela- 
tivity had been discovered. The concepts of space and time be- 
longed both to Newtonian mechanics and to the theory of rela- 
tivity. But space and time in Newtonian mechanics were inde- 
pendent; in the theory of relativity they were connected by the 
Lorentz transformation. In this special case one could show that 
the statements of the theory of relativity approached those of 
Newtonian mechanics within the limit in which all velocities in 
the system are very small as compared with the velocity of light. 
From this one could conclude that the concepts of Newtonian me- 
chanics could not be applied to events in which there oc- 
curred velocities comparable to the velocity of light. Thereby one 
had finally found an essential limitation of Newtonian me- 
chanics which could not be seen from the coherent set of con- 
cepts nor from simple observations on mechanical systems. 

Therefore, the relation between two different coherent sets of 
concepts always requires very careful investigation. Before we 
enter into a general discussion about the structure of any such 
closed and coherent set of concepts and about their possible rela- 
tions we will give a brief description of those sets of concepts that 
have so far been defined in physics. One can distinguish four 
systems that have already attained their final form. 

The first set, Newtonian mechanics, has already been dis- 
cussed. It is suited for the description of all mechanical systems, 
of the motion of fluids and the elastic vibration of bodies; it 
comprises acoustics, statics, aerodynamics. 

The second closed system of concepts was formed in the 
course of the nineteenth century in connection with the theory 
of heat. Though the theory of heat could finally be connected 
with mechanics through the development of statistical me- 
chanics, it would not be realistic to consider it as a part of 
mechanics. Actually the phenomenological theory of heat uses 
a number of concepts that have no counterpart in other branches 
of physics, like: heat, specific heat, entropy, free energy, etc. 
If from this phenomenological description one goes over to a 
statistical interpretation, by considering heat as energy, distri- 
buted statistically among the very many degrees of freedom due 
to the atomic structure of matter, then heat is no more connected 



with mechanics than with electrodynamics or other parts of 
physics. The central concept of this interpretation is the concept 
of probability, closely connected with the concept of entropy 
in the phenomenological theory. Besides this concept the statisti- 
cal theory of heat requires the concept of energy. But any 
coherent set of axioms and concepts in physics will necessarily 
contain the concepts of energy, momentum and angular mo- 
mentum and the law that these quantities must under certain 
conditions be conserved. This follows if the coherent set is in- 
tended to describe certain features of nature that are correct at 
all times and everywhere; in other words, features that do not 
depend on space and time or, as the mathematicians put it, that 
are invariant under arbitrary translations in space and time, 
rotations in space and the Galileo— or Lorentz— transformation. 
Therefore, the theory of heat can be combined with any of the 
other closed systems of concepts. 

The third closed system of concepts and axioms has its origin 
in the phenomena of electricity and magnetism and has reached 
its final form in the first decade of the twentieth century through 
the work of Lorentz. Einstein and Minkowski. It comprises 
electrodynamics, special relativity, optics, magnetism, and one 
may include the de Broglie theory of matter waves of all dif- 
ferent sorts of elementary particles, but not the wave theory of 

Finally, the fourth coherent system is essentially the quantum 
theory as it has been described in the first two chapters. Its 
central concept is the probability function, or the 'statistical 
matrix', as the mathematicians call it. It comprises quantum 
and wave mechanics, the theory of atomic spectra, chemistry, 
and the theory of other properties of matter like electric con- 
ductivity, ferromagnetism, etc. 

The relations between these four sets of concepts can be indi- 
cated in the following way: The first set is contained in the third 
as the limiting case where the velocity of light can be considered 
as infinitely big, and is contained in the fourth as the limiting 
case where Planck's constant of action can be considered as 
infinitely small. The first and partly the third set belong to the 
fourth as a priori for the description of the experiments. The 
second set can be connected with any of the other three sets 


without difficulty and is especially important in its connection 
with the fourth. The independent existence of the third and 
fourth sets suggests the existence of a fifth set, of which one, 
three, and four are limiting cases. This fifth set will probably be 
found someday in connection with the theory of the elementary 

We have omitted from this enumeration the set of concepts 
connected with the theory of general relativity, since this set 
has perhaps noL yet reached its final form. But it should be 
emphasized that it is distinctly different from the other four sets. 

After this short survey we may come back to the more general 
question, what one should consider as the characteristic features 
of such a closed system of axioms and definitions. Perhaps the 
most important feature is the possibility of finding a consistent 
mathematical representation for it. This representation must 
guarantee that the system does not contain contradictions. Then 
the system must be suited to describe a wide field of experience. 
The great variety of phenomena in the field should correspond 
to the great number of solutions of the equations in the mathe- 
matical representation. The limitations of the field can generally 
not be derived from the concepts. The concepts are not sharply 
defined in their relation to nature, in spite of the sharp definition 
of their possible connections. The limitations will therefore be 
found from experience, from the fact that the concepts do not 
allow a complete description of the observed phenomena. 

After this brief analysis of the structure of present-day physics 
the relation between physics and other branches of natural 
science may be discussed. The nearest neighbour to physics is 
chemistry. Actually through quantum theory these two sciences 
have come to a complete union. But a hundred years ago they 
were widely separated, their methods of research were quite 
different, and the concepts of chemistry had at that time no 
counterpart in physics. Concepts like valency, activity, solubility 
and volatility had a more qualitative character, and chemistry 
scarcely belonged to the exact sciences. When the theory of heat 
had been developed by the middle of the last century scientists 
started to apply it to the chemical processes, and ever since then 
the scientific work in this field has been determined by the hope 
of reducing the laws of chemistry to the mechanics of the atoms. 



It should be emphasized, however, that this was not possible I 
within the framework of Newtonian mechanics. In order to give] 
a quantitative description of the laws of chemistry one had to! 
formulate a much wider system of concepts for atomic physics.] 
This was finally done in quantum theory, which has its rootsl 
just as much in chemistry as in atomic physics. Then it was easy! 
to see that the laws of chemistry could not be reduced to New-.l 
tonian mechanics of atomic particles, since the chemical ele-f 
ments displayed in their behaviour a degree of stability com-j 
pletely lacking in mechanical systems. But it was not until Bohr's j 
theory of the atom in 191 3 that this point had been clearly 1 
understood. In the final result, one may say, the concepts of 
chemistry are in part complementary to the mechanical con-l 
cepts. If we know that an atom is in its lowest stationary statei 
that determines its chemical properties we cannot at the samef 
time speak about the motion of the electrons in the atom. 

The present relation between biology, on the one side, and! 
physics and chemistry, on the other, may be very similar to that 1 
between chemistry and physics a hundred years ago. TheT 
methods of biology are different from those of physics and 
chemistry, and the typical biological concepts are of a morel 
qualitative character than those of the exact sciences. Concepts! 
like life, organ, cell, function of an organ, perception have noj 
counterpart in physics or chemistry. On the other hand, most of j 
the progress made in biology during the past hundred years nasi 
been achieved through the application of chemistry and physics 
to the living organism, and the whole tendency of biology in our] 
time is to explain biological phenomena on the basis of the 
known physical and chemical laws. Again the question arises, 
whether this hope is justified or not. 

Just as in the case of chemistry, one learns from simple bio- 
logical experience that the living organisms display a degree of 
stability which general complicated structures consisting of j 
many different types of molecules could certainly not have on the! 
basis of the physical and chemical laws alone. Therefore, some-! 
thing has to be added to the laws of physics and chemistry before 
the biological phenomena can be completely understood. 

With regard to this question two distinctly different views 
have frequently been discussed in the biological literature. The 


one view refers to Darwin's theory of evolution in its connection 
with modern genetics. According to this theory, the only concept 
which has to be added to those of physics and chemistry in order 
to understand life is the concept of history. The enormous time 
interval of roughly four thousand million years that has elapsed 
since the formation of the earth has given nature the possibility 
of trying an almost unlimited variety of structures of groups of 
molecules. Among these structures there have finally been some 
that could reduplicate themselves by using smaller groups from 
the surrounding matter, and such structures therefore could be 
created in great numbers. Accidental changes in the structures 
provided a still larger variety of the existing structures. Different 
structures had to compete for the material drawn from the sur- 
rounding matter and in this way, through the 'survival of the 
fittest,' the evolution of living organisms finally took place. 
There can be no doubt that this theory contains a very large 
amount of truth, and many biologists claim that the addition of 
the concepts of history and evolution to the coherent set of con- 
cepts of physics and chemistry will be amply sufficient to 
account for all biological phenomena. One of the arguments fre- 
quently used in favour of this theory emphasizes that wherever 
the laws of physics and chemistry have been checked in living 
organisms they have always been found to be correct; there 
seems definitely to be no place at which some 'vital force' dif- 
ferent from the forces in physics could enter. 

On the other hand, it is just this argument that has lost much 
of its weight through quantum theory. Since the concepts of 
physics and chemistry form a closed and coherent set, namely, 
that of quantum theory, it is necessary that wherever these con- 
cepts can be used to describe phenomena the laws connected 
with the concepts must be valid too. Therefore, wherever one 
treats living organisms as physicochemical systems, they must 
necessarily act as such. The only question from which we can 
learn something about the adequacy of this first view is whether 
the physicochemical concepts allow a complete description of 
the organisms. Biologists, who answer this question in the nega- 
tive, generally hold the second view, that has now to be ex- 

This second view can perhaps be stated in the following 



terms: It is very difficult to see how concepts like perception,! 
function of an organ, affection could be a part of the coherent 
set of the concepts of quantum theory combined with the con- 
cept of history. On the other hand, these concepts are necessary 
for a complete description of life, even if for the moment we j 
exclude mankind as presenting new problems beyond biology. ! 
Therefore, it will probably be necessary for an understanding of 
life to go beyond quantum theory and to construct a new co- 
herent set of concepts, to which physics and chemistry may be- 
long as 'limiting cases'; History may be an essential part of it, 
and concepts like perception, adaptation, affection also will be- 
long to it. If this view is correct, the combination of Darwin's 
theory with physics and chemistry would not be sufficient to 
explain organic life; but still it would be true that living organ- 
isms can to a large extent be considered as physicochemical sys- 
tems—as machines, as Descartes and Laplace have put it— and 
would, if treated as such, also react as such. One could at the 
same time assume, as Bohr has suggested, that our knowledge of 
a cell being alive may be complementary to the complete knowl- 
edge of its molecular structure. Since a complete knowledge of 
this structure could possibly be achieved only by operations that 
destroy the life of the cell, it is logically possible that life pre- 
cludes the complete determination of its underlying physico- 
chemical structure. Even if one holds this second view one would 
probably recommend for biological research no other method 
than has been pursued in the past decades: attempting to ex- 
plain as much as possible on the basis of the known physico- 
chemical laws, and describing the behaviour of organisms 
carefully and without theoretical prejudices. 

The first of these two views is more common among modern 
biologists than the second; but the experience available at pre- 
sent is certainly not sufficient to decide between the two views. 
The preference that is given by many biologists to the first view 
may be due again to the Cartesian partition, which has pene- 
trated so deeply to the human mind during the past centuries. 
Since the 'res cogitans' was confined to men, to the T, the ani- 
mals could have no soul, they belonged exclusively to the 'res 
extensa'. Therefore, the animals can be understood, so it is 
argued, on the same terms as matter in general, and the laws of 


physics and chemistry together with the concept of history must 
be sufficient to explain their behaviour. It is only when the 'res 
cogitans' is brought in that a new situation arises which will re- 
quire entirely new concepts. But the Cartesian partition is a 
dangerous oversimplification and it is therefore quite possible 
that the second view is the correct one. 

Quite apart from this question, which cannot be settled yet, 
we are obviously still very far from such a coherent and closed 
set of concepts for the description of biological phenomena. The 
degree of complication in biology is so discouraging that one 
can at present not imagine any set of concepts in which the con- 
nections could be so sharply denned that a mathematical repre- 
sentation could become possible. 

If we go beyond biology and include psychology in the discus- 
sion, then there can scarcely be any doubt but that the concepts 
of physics, chemistry, and evolution together will not be suffi- 
cient to describe the facts. On this point the existence of quan- 
tum theory has changed our attitude from what was believed in 
the nineteenth century. During that period some scientists were 
inclined to think that the psychological phenomena could ulti- 
mately be explained on the basis of physics and chemistry of the 
brain. From the quantum-theoretical point of view there is no 
reason for such an assumption. We would, in spite of the fact 
that the physical events in the brain belong to the psychic 
phenomena, not expect that these could be sufficient to explain 
them. We would never doubt that the brain acts as a physico- 
chemical mechanism if treated as such, but for an understanding 
of psychic phenomena we would start from the fact that the 
human mind enters as object and subject into the scientific 
process of psychology. 

Looking back to the different sets of concepts that have been 
formed in the past or may possibly be formed in the future in the 
attempt to find our way through the world by means of science, 
we see that they appear to be ordered by the increasing part 
played by the subjective element in the set. Classical physics can 
be considered as that idealization in which we speak about the 
world as entirely separated from ourselves. The first three sets 
correspond to this idealization. Only the first set complies en- 
tirely with the 'a priori' in the philosophy of Kant. In the fourth 

9 6 


set, that of quantum theory, man as the subject of science is I 
brought in through the questions which are put to nature in 
the a priori terms of human science. Quantum theory does not 
allow a completely objective description of nature. In biology it < 
may be important for a complete understanding that the ques- 
tions are asked by the species man which itself belongs to the 
genus of living organisms, in other words, that we already know 
what life is even before we have denned it scientifically. But one 
should perhaps not enter into speculations about the possible 
structure of sets of concepts that have not yet been formed. 

When one compares this order with older classifications that 
belong to earlier stages of natural science one sees that one has 
now divided the world not into different groups of objects but 
into different groups of connections. In an earlier period of 
science one distinguished, for instance, as different groups 
minerals, plants, animals, men. These objects were taken accord- 
ing to their group as of different natures, made of different ma- 
terials, and determined in their behaviour by different forces. 
Now we know that it is always the same matter, the same various 
chemical compounds that may belong to any object, to minerals 
as well as animals or plants, also the forces that act between the 
different parts of matter are ultimately the same in every kind of 
object. What can be distinguished is the kind of connection 
which is primarily important in a certain phenomenon. For in- 
stance, when we speak about the action of chemical forces we 
mean a kind of connection which is more complicated or in any 
case different from that expressed in Newtonian mechanics. The 
world thus appears as a complicated tissue of events, in which 
connections of different kinds alternate or overlap or combine 
and thereby determine the texture of the whole. 

When we represent a group of connections by a closed and 
coherent set of concepts, axioms, definitions and laws which in 
turn is represented by a mathematical scheme we have in fact 
isolated and idealized this group of connections with the purpose 
of clarification. But even if complete clarity has been achieved in 
this way, it is not known how accurately the set of concepts 
describes reality. 

These idealizations may be called a part of the human lan- 
guage that has been formed from the interplay between the 


world and ourselves, a human response to the challenge of 
nature. In this respect they may be compared to the different 
styles of art, say of architecture or music. A style of art can also 
be defined by a set of formal rules which are applied to the 
material of this special art. These rules can perhaps not be repre- 
sented in a strict sense by a set of mathematical concepts and 
equations, but their fundamental elements are very closely re- 
lated to the essential elements of mathematics. Equality and in- 
equality, repetition and symmetry, certain group structures play 
the fundamental role both in art and in mathematics. Usually 
the work of several generations is needed to develop that formal 
beginning to the wealth of elaborate forms which characterize 
its completion. The interest of the artist is concentrated on this 
system which later is called the style of the art, from its simple 
process of crystallization, where the material of the art takes, 
through his action, the various forms that are initiated by the 
first formal concepts of this style. After the completion the 
interest must fade again, because the word 'interest' means: to 
be with something, to take part in a process of life, but this 
process has then come to an end. Here again the question of how 
far the formal rules of the style represent that reality of life 
which is meant by- the art cannot be decided from the formal 
rules. Art is always an idealization; the ideal is different from 
reality — at least from the reality of the shadows, as Plato would 
have put it — but idealization is necessary for understanding. 

This comparison between the different sets of concepts in 
natural science with different styles of art may seem very far 
from the truth to those who consider the different styles of art 
as rather arbitrary products of the human mind. They would 
argue that in natural science these different sets of concepts 
represent objective reality, have been taught to us by nature, are 
therefore by no means arbitrary, and are a necessary conse- 
quence of our gradually increasing experimental knowledge of 
nature. About these points most scientists would agree; but are 
the different styles of art an arbitrary product of the human 
mind? Here again we must not be misled by the Cartesian 
Partition. The style arises out of the interplay between the world 
and ourselves, or more specifically between the spirit of the time 
and the artist. The spirit of a time is probably a fact as objective 

9 8 


as any fact in natural science, and this spirit brings out certai^ 
features of the world which are even independent of time, ar 
in this sense eternal. The artist tries by his work to make thes 
features understandable, and in this attempt he is led to th| 
forms of the style in which he works. 

Therefore, the two processes, that of science and that of ar 
are not very different. Both science and art form in the course < 
the centuries a human language by which we can speak abou| 
the more remote parts of reality, and the coherent sets of cor 
cepts as well as the different styles of art are different words - 
groups of words in this language. 

The Theory of Relativity 

WITHIN the field of modern physics the theory of relativity has 
always played a very important role,. It was in this theory that the 
necessity for a change in the fundamental principles of physics 
was recognized for the first time. Therefore, a discussion of those 
problems that had been raised and partly solved by the theory of 
relativity belongs essentially to our treatment of the philosophi- 
cal implications of modern physics. In some sense it may be said 
that — contrary to quantum theory — the development of the 
theory of relativity from the final recognition of the difficulties 
to their solution has taken only a very short time. The repetition 
of Michelson's experiment by Morley and Miller in 1904 was the 
first definite evidence for the impossibility of detecting the trans- 
lational motion of the earth by optical methods, and Einstein's 
decisive paper appeared less than two years later. On the other 
hand, the experiment of Morley and Miller and Einstein's paper 
were only the final steps in a development which had started 
very much earlier and which may be summarized under the 
heading 'electrodynamics of moving bodies'. 

Obviously the electrodynamics of moving bodies had been an 
important field of physics and engineering ever since electro- 
motors had been constructed. A serious difficulty had been 
brought into this subject, however, by Maxwell's discovery of 
the electromagnetic nature of light waves. These waves differ in 
one essential property from other waves, for instance, from 
sound waves: they can be propagated in what seems to be 
empty space. When a bell rings in a vessel that has been evacu- 
ated, the sound does not penetrate to the outside. But light does 
penetrate easily through the evacuated volume. Therefore, one 
assumed that light waves could be considered as elastic waves of 





a very light substance called ether which could be neither seen 
nor felt but which filled the evacuated space as well as the space 
in which other matter, like air or glass, existed. The idea that 
electromagnetic waves could be a reality in themselves, inde- 
pendent of any bodies, did at that time not occur to the physi- 
cists. Since this hypothetical substance ether seemed to penetrate 
through other matter, the question arose: What happens if the 
matter is set into motion? Does the ether participate in this 
motion and — if this is the case — how is a light wave propagated 
in the moving ether? 

Experiments which are relevant to this question are difficult 
for the following reason: The velocities of moving bodies are 
usually very small compared to the velocity of light. Therefore, 
the motion of these bodies can only produce very small effects 
which are proportional to the ratio of the velocity of the body 
to the velocity of light, or to a higher power of this ratio. Several 
experiments by Wilson, Rowland, Roentgen and Eichenwald 
and Fizeau permitted the measurement of such effects with an 
accuracy corresponding to the first power of this ratio. The 
theory of the electrons developed by Lorentz in 1895 was able to ; 
describe these effects quite satisfactorily. But then the experi- 
ment of Michelson, Morley and Miller created a new situation. 
This experiment shall be discussed in some detail. In order to 
get bigger effects and thereby more accurate results, it seemed 
best to do experiments with bodies of very high velocity. The 
earth moves around the sun with a velocity of roughly 20 
miles/sec. If the ether is at rest with respect to the sun and does 
not move with the earth, then this fast motion of the ether with 
respect to the earth should make itself felt in a change of the 
velocity of light. This velocity should be different depending on 
whether the light is propagated in a direction parallel or per- 
pendicular to the direction of the motion of the ether. Even if 
the ether should partly move with the earth, there should be 
some effect due to what one may call wind of the ether, and this 
effect would then probably depend on the altitude above sea j 
level at which the experiment is carried out. A calculation of '< 
the expected effect showed that it should be very small, since it 
is proportional to the square of the ratio of the velocity of the 
earth to that of the light, and that one therefore had to carry out 

very careful experiments on the interference of two beams of 
light traveling parallel or perpendicular to the motion of the 
earth. The first experiment of this kind, carried out by Michel- 
son in 1 88 1, had not been sufficiently accurate. But even later 
repetitions of the experiment did not reveal the slightest signs 
of the expected effect. Especially the experiments of Morley and 
Miller in 1904 could be considered as definite proof that an effect 
of the expected order of magnitude did not exist. 

This result, strange as it was, met another point that had been 
discussed by the physicists some time before. In Newton's me- 
chanics a certain 'principle of relativity' is fulfilled that can be 
described in the following terms: If in a certain system of ref- 
erence the mechanical motion of bodies fulfills the laws of New- 
tonian mechanics then this is also true for any other frame of 
reference which is in uniform nonrotating motion with respect 
to the first system. Or, in other words, a uniform translational 
motion of a system does not produce any mechanical effects at 
all and can therefore not be observed by such effects. 

Such a principle of relativity — so it seemed to the physicists — 
could not be true in optics or electrodynamics. If the first system 
is at rest with respect to the ether, the other systems are not, and 
therefore their motion with respect to the ether should be recog- 
nized by effects of the type considered by Michelson. The nega- 
tive result of the experiment of Morley and Miller in 1904 re- 
vived the idea that such a principle of relativity could be true in 
electrodynamics as well as Newtonian mechanics. 

On the other hand, there was an old experiment by Fizeau in 
1 85 1 that seemed definitely to contradict the principle of rela- 
tivity. Fizeau had measured the velocity of light in a moving 
liquid. If the principle of relativity was correct, the total velocity 
of light in the moving liquid should be the sum of the velocity of 
the liquid and the velocity of light in the liquid at rest. But this 
was not the case; the experiment of Fizeau snowed that the total 
velocity was somewhat smaller. 

Still the negative results of all more recent experiments to 
recognize the motion 'with respect to the ether' inspired the 
theoretical physicists and mathematicians at that time to look for 
mathematical interpretations that reconciled the wave equation 
for the propagation of light with the principle of relativity. 






Lorentz suggested, in 1904, a mathematical transformation thai 
fulfilled these requirements. He had to introduce the hypothesis] 
that moving bodies are contracted in the direction of motion by? 
a factor depending on the velocity of the body, and in different! 
schemes of reference there are different 'apparent' times whichj 
in many ways take the place of the 'real' time. In this way he 
could represent something resembling the principle of relativity: 
the 'apparent' velocity of light was the same in every system of 
reference. Similar ideas had been discussed by Poincare, Fitz- 
gerald and other physicists. 

This decisive step, however, was taken in the paper by Einstein 
in 1905 in which he established the 'apparent' time of the 
Lorentz transformation as the 'real' time and abolished what 
had been called 'real' time by Lorentz. This was a change in 
the very foundations of physics; an unexpected and very radical 
change that required all the courage of a young and revolution- 
ary genius. To take this step one needed, in the mathematical | 
representation of nature, nothing more than the consistent ap- 
plication of the Lorentz transformation. But by its new inter- 1 
pretation the structure of space and time had changed and 
many problems of physics appeared in a new light. The sub- 
stance ether, for instance, could be abolished too. Since all sys- 
tems of reference that are in uniform translation motion with j 
respect to each other are equivalent for the description of nature, 
there is no meaning in the statement that there is a substance, 
the ether, which is at rest in only one of these systems. Such a 
substance is in fact not needed and it is much simpler to say that 
light waves are propagated through empty space and that 
electromagnetic fields are a reality of their own and can exist in 
empty space. 

But the decisive change was in the structure of space and time. 
It is very difficult to describe this change in the words of 
common language without the use of mathematics, since the 
common words 'space' and 'time' refer to a structure of space 
and time that is actually an idealization and oversimplification 
of the real structure. But still we have to try to describe the new 
structure and we can perhaps do it in the following way: 

When we use the term 'past' we comprise all those events 
which we could know at least in principle, about which we could 


have heard at least in principle. In a similar manner we com- 
prise by the term 'future' all those events which we could in- 
fluence at least in principle, which we could try to change or to 
prevent at least in principle. It is not easy for a nonphysicist to 
see why this definition of the terms 'past' and 'future' should 
be the most convenient one. But one can easily see that it corre- 
sponds very accurately to our common use of the terms. If we 
use the terms in this way, it turns out as a result of many experi- 
ments that the content of 'future' or 'past' does not depend on 
the state of motion or other properties of the observer. We may 
say that the definition is invariant against the motion of the 
observer. This is true both in Newtonian mechanics and in Ein- 
stein's theory of relativity. 

But the difference is this: In classical theory we assume that 
future and past are separated by an infinitely short time interval 
which we may call the present moment. In the theory of rela- 
tivity we have learned that the situation is different: future and 
past are separated by a finite time interval the length of which 
depends on the distance from the observer. Any action can only 
be propagated by a velocity smaller than or equal to the velocity 
of light. Therefore, an observer can at a given instant neither 
know of nor influence any event at a distant point which takes 
place between two characteristic times. The one time is the 
instant at which a light signal has to be given from the point of 
the event in order to reach the observer at the instant of observa- 
tion. The other time is the instant at which a light signal, given 
by the observer at the instant of the observation, reaches the 
point of the event. The whole finite time interval between these 
two instants may be said to belong to the 'present time' for the 
observer at the instant of observation. Any event taking place 
beween the two characteristic times may be called 'simultaneous' 
with the act of observation. 

The use of the phrase 'may be called' points up an ambiguity 
in the word 'simultaneous', which is due to the fact that this 
term has been formed from the experience of daily life, in which 
the velocity of light can always be considered as infinitely high. 
Actually this term in physics can be defined also in a slightly dif- 
ferent manner and Einstein has in his papers used this second 
definition. When two events happen at the same point in space 





simultaneously, we say that they coincide; this term is quite 
unambiguous. Let us now imagine three points in space that lie;] 
on a straight line so that the point in the middle has the samej 
distance from each of the two outer points. If two events happen; 
at the two outer points at such times that light signals starting! 
from the events coincide when they reach the point in the 
middle, we can define the two events as simultaneous. This 
definition is narrower than the first one. One of its most im- 
portant consequences is that when two events are simultaneous 
for one observer they may not be simultaneous for another 
observer, if he is in motion relative to the first observer. The con- 
nection between the two definitions can be established by the 
statement that whenever two events are simultaneous in the first 
sense of the term, one can always find a frame of reference in 
which they are simultaneous in the second sense too. 

The first definition of the term 'simultaneous' seems to corre- 
spond more nearly to its use in daily life, since the question 
whether two events are simultaneous does in daily life not de- 
pend on the frame of reference. But in both relativistic defini- 
tions the term has acquired a precision which is lacking in the 
language of daily life. In quantum theory the physicists had to 
learn rather early that the terms of classical physics describe 
nature only inaccurately, that their application is limited by 
the quantum laws' and that one therefore should be cautious in 
their use. In the theory of relativity the physicists have tried to 
change the meaning of the words of classical physics, to make 
the terms more precise in such a way that they fit the new situa- 
tion in nature. 

The structure of space and time that has been brought to 
light by the theory of relativity has many consequences in dif- 
ferent parts of physics. The electrodynamics of moving bodies 
can be derived at once from the principle of relativity. This 
principle itself can be formulated as a quite general law of nature 
pertaining not only to electrodynamics or mechanics but to any 
group of laws: The laws take the same form in all systems of 
reference, which are different from each other only by a uniform 
translational motion; they are invariant against the Lorentz 

Perhaps the most important consequence of the principle of 

relativity is the inertia of energy, or the equivalence of mass and 
energy. Since the velocity of light is the limiting velocity which 
can never be reached by any material body, it is easy to see that 
it is more difficult to accelerate a body that is already moving 
very fast than a body at rest. The inertia has increased with the 
kinetic energy. But quite generally any kind of energy will, 
according to the theory of relativity, contribute to the inertia, 
i.e., to the mass, and the mass belonging to a given amount of 
energy is just this energy divided by the square of the velocity 
of light. Therefore, every energy carries mass with it; but even a 
rather big energy carries only a very small mass, and this is the 
reason why the connection between mass and energy had not 
been observed before. The two laws of the conservation of mass 
and the conservation of charge lose their separate validity and 
are combined into one single law which may be called the law of 
conservation of energy or mass. Fifty years ago, when the theory 
of relativity was formulated, this hypothesis of the equivalence 
of mass and energy seemed to be a complete revolution in 
physics, and there was still very little experimental evidence for 
it. In our times we see in many experiments how elementary 
particles can be created from kinetic energy, and how such 
particles are annihilated to form radiation; therefore, the trans- 
mutation from energy into mass and vice versa suggests nothing 
unusual. The enormous release of energy in an atomic explosion 
is another and still more spectacular proof of the correctness of 
Einstein's equation. But we may add here a critical historical 

It has sometimes been stated that the enormous energies of 
atomic explosions are due to a direct transmutation of mass into 
energy, and that it is only on the basis of the theory of relativity 
that one has been able to predict these energies. This is, however, 
a misunderstanding. The huge amount of energy available in the 
atomic nucleus was known ever since the experiments of Bec- 
querel, Curie and Rutherford on radioactive decay. Any decay- 
ing body like radium produces an amount of heat about a 
million times greater than the heat released in a chemical process 
in a similar amount of material. The source of energy in the 
fission process of uranium is just the same as that in the a-decay 
of radium, namely, mainly the electrostatic repulsion of the two 





parts into which the nucleus is separated. Therefore, the energy 
of an atomic explosion comes directly from this source and is 
not derived from a transmutation of mass into energy. The i 
number of elementary particles with finite rest mass does not de- 
crease during the explosion. But it is true that the binding ener- 
gies of the particles in an atomic nucleus do show up in their 
masses and therefore the release of energy is in this indirect 
manner also connected with changes in the masses of the nuclei. 
The equivalence of mass and energy has— besides its great im- 
portance in physics— also raised problems concerning very old 
philosophical questions. It has been the thesis of several philo- 
sophical systems of the past that substance or matter cannot be 
destroyed. In modern physics, however, many experiments have 
shown that elementary particles, e.g., positrons and electrons, 
can be annihilated and transmuted into radiation. Does this mean 
that these older philosophical systems have been disproved by 
modern experience and that the arguments brought forward by 
the earlier systems have been misleading? 

This would certainly be a rash and unjustified conclusion, 
since the terms 'substance* and 'matter* in ancient or medieval 
philosophy cannot simply be identified with the term 'mass' in 
modern physics. If one wished to express our modern experience 
in the language of older philosophies, one could consider mass 
and energy as two different forms of the same 'substance' and 
thereby keep the idea of substance as indestructible. 

On the other hand, one can scarcely say that one gains much 
by expressing modern knowledge in an old language. The 
philosophic systems of the past were formed from the bulk of 
knowledge available at their time and from the lines of thought 
to which such knowledge had led. Certainly one should not 
expect the philosophers of many hundreds of years ago to have 
foreseen the development of modern physics or the theory of 
relativity. Therefore, the concepts to which the philosophers 
were led in the process of intellectual clarification a long time 
ago cannot possibly be adapted to phenomena that can only be 
observed by the elaborate technical tools of our time. 

But before going into a discussion of philosophical implica- 
tions of the theory of relativity its further development has to be 

The hypothetical substance 'ether', which had played such 
an important role in the early discussions on Maxwell's theories 
in the nineteenth century, had — as has been said before — been 
abolished by the theory of relativity. This is sometimes stated by 
saying that the idea of absolute space has been abandoned. But 
such a statement has to be accepted with great caution. It is true 
that one cannot point to a special frame of reference in which the 
substance ether is at rest and which could therefore deserve the 
name 'absolute space'. But it would be wrong to say that space 
has now lost all of its physical properties. The equations of 
motion for material bodies or fields still take a different form in 
a 'normal' system of reference from another one which rotates 
or is in a nonuniform motion with respect to the 'normal' one. 
The existence of centrifugal forces in a rotating system proves — 
so far as the theory of relativity of 1905 and 1906 is concerned — 
the existence of physical properties of space which permit the 
distinction between a rotating and a nonrotating system. 

This may not seem satisfactory from a philosophical point of 
view, from which one would prefer to attach physical properties 
only to physical entities like material bodies or fields and not to 
empty space. But so far as the theory of electromagnetic proc- 
esses or mechanical motions is concerned, this existence of 
physical properties of empty space is simply a description of facts 
than cannot be disputed. 

A careful analysis of this situation about ten years later, in 
1916, led Einstein to a very important extension of the theory of 
relativity, which is usually called the theory of 'general rela- 
tivity'. Before going into a description of the main ideas of this 
new theory it may be useful to say a few words about the degree 
of certainty with which we can rely on the correctness of these 
two parts of the theory of relativity. The theory of 1905 and 
1906 is based on a very great number of well-established facts: 
on the experiments of Michelson and Morley and many similar 
ones, on the equivalence of mass and energy in innumerable 
radioactive processes, on the dependence of the lifetime of radio- 
active bodies on their velocity, etc. Therefore, this theory be- 
longs to the firm foundations of modern physics and cannot be 
disputed in our present situation. 

For the theory of general relativity the experimental evidence 





is much less convincing, since the experimental material is very; 
scarce. There are only a few astronomical observations which 
allow a checking of the correctness of the assumptions. There- 1 
fore, this whole theory is more hypothetical than the first one . 

The cornerstone of the theory of general relativity is the con-, 
nection between inertia and gravity. Very careful measurements 
have shown that the mass of a body as a source of gravity is 
exactly proportional to the mass as a measure for the inertia of 
the body. Even the most accurate measurements have never 
shown any deviation from this law. If the law is generally true, 
the gravitational forces can be put on the same level with the| 
centrifugal forces or with other forces that arise as a reaction of 
the inertia. Since the centrifugal forces had to be considered as| 
due to physical properties of empty space, as had been discussed 
before, Einstein turned to the hypothesis that the gravitational 
forces also are due to properties of empty space. This was a very 
important step which necessitated at once a second step of equal 
importance. We know that the forces of gravity are produced by 1 
masses. If therefore gravitation is connected with properties of] 
space, these properties of space must be caused or influenced by 
the masses. The centrifugal forces in a rotating system must be ■ 
produced by the rotation (relative to the system) of possibly 
very distant masses. 

In order to carry out the programme outlined in these few sen- 
tences Einstein had to connect the underlying physical ideas with 
the mathematical scheme of general geometry that had been de- 
veloped by Riemann. Since the properties of space seemed to 
change continuously with the gravitational fields, its geometry 
had to be compared with the geometry on curved surfaces where 
the straight line of Euclidean geometry has to be replaced by the 
geodetical line, the line of shortest distance, and where the 
curvature changes continuously. As a final result Einstein was 
able to give a mathematical formulation for the connection be- 
tween the distribution of masses and the determining parameters 
of the geometry. This theory did represent the common facts 
about gravitation. It was in a very high approximation identical 
with the conventional theory of gravitation and predicted 
furthermore a few interesting effects which were just at the limit 
of measurability. There was, for instance, the action of gravity 

on light. When monochromatic light is emitted from a heavy 
star, the light quanta lose energy when moving away through the 
gravitational field of the star; a red shift of the emitted spectral 
line follows. There is as yet no experimental evidence for this 
red shift, as the discussion of the experiments by Freundlich has 
clearly shown. But it would also be premature to conclude that 
the experiments contradict the prediction of Einstein's theory. 
A beam of light that passes near the sun should be deflected by 
its gravitational field. The deflection has been found experi- 
mentally by Freundlich in the right order of magnitude; but 
whether the deflection agrees quantitatively with the value pre- 
dicted by Einstein's theory has not yet been decided. The best 
evidence for the validity of the theory of general relativity seems 
to be the procession in the orbital motion of the planet Mercury, 
which apparently is in very good agreement with the value pre- 
dicted by the theory. 

Though the experimental basis of general relativity is still 
rather narrow, the theory contains ideas of the greatest im- 
portance. During the whole period from the mathematicians of 
ancient Greece to the nineteenth century, Euclidean geometry 
had been considered as evident; the axioms of Euclid were re- 
garded as the foundation of any mathematical geometry, a 
foundation that could not be disputed. Then, in the nineteenth 
century, the mathematicians Bolyai and Lobachevsky, Gauss 
and Riemann found that other geometries could be invented 
which could be developed with the same mathematical precision 
as that of Euclid; therefore, the questions as to which geometry 
was correct turned out to be an empirical one. But it was only 
through the work of Einstein that the question could really be 
taken up by the physicists. The geometry discussed in the theory 
of general relativity was not concerned with three-dimensional 
space only but with the four-dimensional manifold consisting of 
space and time. The theory established a connection between the 
geometry in this manifold and the distribution of masses in the 
world. Therefore, this theory raised in an entirely new form the 
old questions of the behaviour of space and time in the largest 
dimensions; it could suggest possible answers that could be 
checked by observations. 

Consequently, very old philosophic problems were taken up 





that had occupied the mind of man since the earliest phases of| 
philosophy and science. Is space finite or infinite? What was! 
there before the beginning of time? What will happen at the end] 
of time? Or is there no beginning and no end? These questions had] 
found different answers in different philosophies and re-f 
ligions. In the philosophy of Aristotle, for instance, the total''] 
space of the universe was finite (though it was infinitely divis-^ 
ible) . Space was due to the extension of bodies, it was con- 
nected with the bodies; there was no space where there were no i 
bodies. The universe consisted of the earth and the sun and the, 
stars: a finite number of bodies. Beyond the sphere of the stars 
there was no space; therefore, the space of the universe was 

In the philosophy of Kant this question belonged to what he ■ 
called 'antinomies' — questions that cannot be answered, since } 
two different arguments lead to opposite results. Space cannot] 
be finite, since we cannot imagine that there should be an end| 
to space; to whichever point in space we come we can always | 
imagine that we can go beyond. At the same time space cannot| 
be infinite, because space is something that we can imagine (else ; 
the word 'space' would not have been formed) and we cannot' 
imagine an infinite space. For this second thesis the argument of 
Kant has not been verbally reproduced. The sentence 'space is 
infinite' means for us something negative; we cannot come to 
an end of space. For Kant it means that the infinity of space 
is really given, that it 'exists' in a sense that we can scarcely 
reproduce. Kant's result is that a rational answer to the ques- 
tion whether space is finite or infinite cannot be given because 
the whole universe cannot be the object of our experience. 

A similar situation is found with respect to the problem of the 
infinity of time. In the Confessions of St. Augustine, for instance, 
this question takes the form: What was God doing before He 
created the world? Augustine is not satisfied with the joke: 
'God was busy preparing Hell for those who ask foolish ques- 
tions.' This, he says, would be too cheap an answer, and he tries 
to give a rational analysis of the problem. Only for us is time 
passing by; it is expected by us as future; it passes by as the 
present moment and is remembered by us as past. But God is not 
in time; a thousand years are for Him as one day, and one day as 

a thousand years. Time has been created together with the 
world, it belongs to the world, therefore time did not exist be- 
fore the universe existed. For God the whole course of the uni- 
verse is given at once. There is no time before He created the 
world. It is obvious that in such statements the word 'created' 
at once raises all the essential difficulties. This word as it is usually 
understood means that something has come into being that has 
not been before, and in this sense it presupposes the concept of 
time. Therefore, it is impossible to define in rational terms what 
could be meant by the phrase 'time has been created'. This fact 
reminds us again of the often discussed lesson that has been 
learned from modern physics: that every word or concept, clear 
as it may seem to be, has' only a limited range of applicability. 

In the theory of general relativity these questions about the 
infinity of space and time can be asked and partly answered on 
an empirical basis. If the connection between the four-dimen- 
sional geometry in space and time and the distribution of masses 
in the universe has been correctly given by the theory, then the 
astronomical observations on the distribution of galaxies in space 
give us information about the geometry of the universe as a 
whole. At least one can build 'models' of the universe, cos- 
mological pictures, the consequences of which can be compared 
with the empirical facts. 

From the present astronomical knowledge one cannot defi- 
nitely distinguish between several possible models. It may be 
that the space filled by the universe is finite. This would not 
mean that there is an end of the universe at some place. It would 
only mean that by proceeding farther and farther in one direc- 
tion in the universe one would finally come back to the point 
from which one had started. The situation would be similar as 
in the two-dimensional geometry on the surface of the earth 
where we, when starting from a point in an eastward direction, 
finally come back to this point from the west. 

With respect to time there seems to be something like a begin- 
ning. Many observations point to an origin of the universe about 
four billion years ago; at least they seem to show that at that 
time all matter of the universe was concentrated in a much 
smaller space than it is now and has expanded ever since from 
this small space with different velocities. The same time of four 





billion years is found in many different observations (e.g., from 
the age of meteorites, of minerals on the earth, etc.), and there-] 
fore it would be difficult to find an interpretation essentially dif- 
ferent from this idea of an origin. If it is the correct one it would 
mean that beyond this time the concept of time would undergo 
essential changes. In the present state of astronomical observa- 
tions the questions about the space-time geometry on a large 
scale cannot yet be answered with any degree of certainty. But it 
is extremely interesting to see that these questions may possibly f 
be answered eventually on a solid empirical basis. For the time>] 
being even the theory of general relativity rests on a very narrow 
experimental foundation and must be considered as much less 
certain than the so-called theory of special relativity expressed 
by the Lorentz transformation. 

Even if one limits the further discussions of this latter theoryf 
there is no doubt that the theory of relativity has deeply changed| 
our views on the structure of space and time. The most exciting 
aspect of these changes is perhaps not their special nature butj 
the fact that they have been possible. The structure of space and| 
time which had been defined by Newton as the basis of hif 
mathematical description of nature was simple and consistent 
and corresponded very closely to the use of the concepts space! 
and time in daily life. This correspondence was in fact so close] 
that Newton's definitions could be considered as the precise 
mathematical formulation of these common concepts. Before thel 
theory of relativity it seemed completely obvious 1 that events 
could be ordered in time independent of their location in space. 
We know now that this impression is created in daily life by the 
fact that the velocity of light is so very much higher than any 
other velocity occurring in practical experience; but this restric- 
tion was of course not realized at that time. And even if we know 
the restriction now we can scarcely imagine that the time order 
of events should depend on their location. 

The philosophy of Kant later on drew attention to the fact 
that the concepts of space and time belong to our relation to 
nature, not to nature itself; that we could not describe nature 
without using these concepts. Consequently, these concepts are 
'a priori' in some sense, they are the condition for and not 
primarily the result of experience, and it was generally believed 

that they could not be touched by new experience. Therefore, 
the necessity of the change appeared as a great surprise. It was 
the first time that the scientists learned how cautious they had to 
be in applying the concepts of daily life to the refined experience 
of modern experimental science. Even the precise and consistent 
formulation of these concepts in the mathematical language of 
Newton's mechanics or their careful analysis in the philosophy 
of Kant had offered no protection against the critical analysis 
possible through extremely accurate measurements. This warn- 
ing later proved extremely useful in the development of modern 
physics, and it would certainly have been still more difficult to 
understand quantum theory had not the success of the theory of 
relativity warned the physicists against the uncritical use of con- 
cepts taken from daily life or from classical physics*. 


Criticism and Counterproposals to the 

Copenhagen Interpretation of 

Quantum Theory 

THE Copenhagen interpretation of quantum theory has led th<j 
physicists far away from the simple materialistic views that pr ' 
vailed in the natural science of the nineteenth century. Sine 
these views had not only been intrinsically connected wit 
natural science of that period but had also found a systematic 
analysis in some philosophic systems and had penetrated deeplj 
into the mind even of the common men on the street, it can " 
well understood that many attempts have been made to critiriaj 
the Copenhagen interpretation and to replace it by one more 
line with the concepts of classical physics or materialistic pi 

These attempts can be divided into three different grouf 
The first group does not want to change the Copenhagen ii 
terpretation so far as predictions of experimental results' are conl 
cerned; but it tries to change the language of this interpretatior 
in order to get a closer resemblance to classical physics. In othe 
words, it tries to change the philosophy without changing th< 
physics. Some papers of this first group restrict their agreement 
with the experimental predictions of the, Copenhagen interpret 
tion to all those experiments that have hitherto been carried 01 
or that belong to normal electronic physics. 

The second group realizes that the Copenhagen interpretation! 
is the only adequate one, if the experimental results agree every- 
where with the predictions of this interpretation. Therefore, the j 
papers of this group try to change quantum theory to some 


extent in certain critical points. 

The third group, finally, expresses rather its general dissatis- 
faction with the results of the Copenhagen interpretation and 
especially with its philosophical conclusions, without making 
definite counterproposals. Papers by Einstein, von Laue and 
Schrodinger belong to this third group which has historically 
been the first of the three groups. 

However, all the opponents of the Copenhagen interpretation 
do agree on one point. It would, in their view, be desirable to 
return to the reality concept of classical physics or, to use a more 
general philosophic term, to the ontology of materialism. They 
would prefer to come back to the idea of an objective real world 
whose smallest parts exist objectively in the same sense as stones 
or trees exist, independently of whether or not we observe them. 

This, however, is impossible or at least not entirely possible 
because of the nature of the atomic phenomena, as has been dis- 
cussed in some of the earlier chapters. It cannot be our task to 
formulate wishes as to how the atomic phenomena should be; 
our task can only be to understand them. 

When one analyzes the papers of the first group, it is im- 
portant to realize from the beginning that their interpretations 
cannot be refuted by experiment, since they only repeat the 
Copenhagen interpretation in a different language. From a 
strictly positivistic standpoint one may even say that we are here 
concerned not with counterproposals to the Copenhagen in- 
terpretation but with its exact repetition in a different language. 
Therefore, one can only dispute the suitability of this language. 
One group of counterproposals works with the idea of 'hidden 
parameters'. Since the quantum-theoretical laws determine in 
general the results of an experiment only statistically, one would 
from the classical standpoint be inclined to think that there exist 
tome hidden parameters which escape observation in any 
ordinary experiment but which determine the outcome of the 
experiment in the normal causal way. Therefore, some papers 
try to construct such parameters within the framework of quan- 
tum mechanics. 

Along this line, for instance, Bohm has made a counter- 
Proposal to the Copenhagen interpretation, which has recently 
been taken up to some extent also by de Broglie. Bohm's in- 



terpretation has been worked out in detail. It may therefore 
serve here as a basis for the discussions. Bohm considers the par- 
ticles as 'objectively real' structures, like the point masses in] 
Newtonian mechanics. The waves in configuration space are in 
his interpretation 'objectively real' too, like electric fields. Con-- 
figuration space is a space of many dimensions referring to the 
different co-ordinates of all the particles belonging to the system. 
Here we meet a first difficulty: what does it mean to call waves 
in configuration space 'real'? This space is a very abstract 
space. The word 'real' goes back to the Latin word, 'res', 
which means 'thing'; but things are in the ordinary three- 
dimensional space, not in an abstract configuration space. One 
may call the waves in configuration space 'objective' when one 
wants to say that these waves do not depend on any observer;; 
but one can scarcely call them 'real' unless one is willing tOi 
change the meaning of the word. Bohm goes on defining the- 
lines perpendicular to the surfaces of constant wave-phase as the 
possible orbits of the particles. Which of these lines is the 'rear 
orbit depends, according to him, on the history of the system 
and the measuring apparatus and cannot be decided without 
knowing more about the system and the measuring equipment 
than actually can be known. This history contains in fact the 
hidden parameters, the 'actual orbit' before the experiment, 

One consequence of this interpretation is, as Pauli has empha- 
sized, that the electrons in the ground states ofmanyatomSj 
should be at rest, not performing any orbital motion around the 
atomic nucleus. This looks like a contradiction of the experi- 
ments, since measurements of the velocity of the electrons in the! 
ground state (for instance, by means of the Compton effect) 
reveal always a velocity distribution in the ground state, which 
is — in conformity with the rules of quantum mechanics — given 
by the square of the wave function in momentum or velocity 
space. But here Bohm can argue that the measurement can no 
longer be evaluated by the ordinary laws. He agrees that the 
normal evaluation of the measurement would indeed lead to a 
velocity distribution; but when the quantum theory for the 
measuring equipment is taken into account — especially some 
strange quantum potentials introduced ad hoc by Bohm — then 


the statement is admissible that the electrons 'really' always are 
at rest. In measurements of the position of the particle, Bohm 
takes the ordinary interpretation of the experiments as correct; 
in measurements of the velocity he rejects it. At this price Bohm 
considers himself able to assert: 'We do not need to abandon 
the precise, rational and objective description of individual 
systems in the realm of quantum theory.' This objective descrip- 
tion, however, reveals itself as a kind of 'idealogical super- 
structure', which has little to do with immediate physical 
reality; for the hidden parameters of Bohm's interpretation are 
of such a kind that they can never occur in the description of 
real processes, if quantum theory remains unchanged. 

In order to escape this difficulty, Bohm does in fact express 
the hope that in future experiments in the range of the ele- 
mentary particles the hidden parameters may yet play a physical 
part, and that quantum theory may thus be proved false. When 
such strange hopes were expressed, Bohr used to say that they 
were similar in structure to the sentence: 'We may hope that 
it will later turn out that sometimes 2 x 2 = 5, for this would 
be of great advantages for our finances. Actually the fulfilment 
of Bohm's hopes would cut the ground from beneath not only 
quantum theory but also Bohm's interpretation. Of course it 
must at the same time be emphasized that the analogy just men- 
tioned, although complete, does not represent a logically com- 
pelling argument against a possible future alteration of quantum 
theory in the manner suggested by Bohm. For it would not be 
fundamentally unimaginable that, for example, a future exten- 
sion of mathematical logic might give a certain meaning to the 
statement that in exceptional cases 2x2 = 5, and it might 
even be possible that this extended mathematics would be of use 
in calculations in the field of economics. We are nevertheless 
actually convinced, even without cogent logical grounds, that 
such changes in mathematics would be of no help to us finan- 
cially. Therefore, it is very difficult to understand how the 
mathematical proposals which the work of Bohm indicates as a 
possible realization of his hopes could be used for the description 
of physical phenomena. 

If we disregard this possible alteration of quantum theory, 
then Bohm's language, as we have already pointed out, says 



nothing about physics that is different from what the Copen- 
hagen interpretation says. There then remains only the question 
of the suitability of this language. Besides the objection already 
made that in speaking of particle orbits we are concerned with a 
superflous 'ideological superstructure', it must be particularly 
mentioned here that Bohm's language destroys the symmetry be- 
tween position and velocity which is implicit in quantum theory; 
for the measurements of position Bohm accepts the usual in- 
terpretation, for the measurements of velocity or momentum he 
rejects it. Since the symmetry properties always constitute the 
most essential features of a theory, it is difficult to see what 
would be gained by omitting them in the corresponding lan- 
guage. Therefore, one cannot consider Bohm's counterproposal 
to the Copenhagen interpretation as an improvement. 

A similar objection can be raised in a somewhat different 
form against the statistical interpretations put forward by Bopp 
and (on a slightly different line) by Fenyes. Bopp considers the 
creation or the annihilation of a particle as the fundamental 
process of quantum theory, the particle is 'real' in the classical 
sense of the word, in the sense of materialistic ontology, and the 
laws of quantum theory are considered as a special case of 
correlation statistics for such events of creation and annihilation. 
This interpretation, which contains many interesting comments 
on the mathematical laws of quantum theory, can be carried out 
in such a manner that it leads, as regards the physical conse- 
quences, to exactly the same conclusions as the Copenhagen 
interpretation. So far it is, in the positivistic sense, isomorphic 
with it, as is Bohm's. But in its language it destroys the symmetry 
between particles and waves that otherwise is a characteristic 
feature of the mathematical scheme of quantum theory. As early 
as 1928 it was shown by Jordan, Klein and Wigner that the 
mathematical scheme can be interpreted not only as a quantiza- 
tion of particle motion but also as a quantization of three- 
dimensional matter waves; therefore, there is no reason to 
consider these matter waves as less real than the particles. The 
symmetry between waves and particles could be ensured in 
Bopp's interpretation only if the corresponding correlation statis- 
tics were developed for matter waves in space and time as well, 
and if the question was left open whether particles or waves are 


to be considered as the 'actual' reality. 

The assumption that particles are real in the sense of the ma- 
terialistic ontology will always lead to the temptation to con- 
sider deviations from the uncertainty principle as 'basically' 
possible. Fenyes, for instance, says that 'the existence of the 
uncertainty principle [which he connect with certain statistical 
relations] by no means renders impossible the simultaneous 
measurement, with arbitrary accuracy, of position and velocity.' 
Fenyes does not, however, state how such measurements should 
be carried out in practice, and therefore his considerations seem 
to remain abstract mathematics. 

Weizel, whose counterproposals to the Copenhagen in- 
terpretation are akin to those of Bohm and Fenyes, relates the 
'hidden parameters' to a new kind of particle introduced ad 
hoc, the 'zeron', which is not otherwise observable. However, 
such a concept runs into the danger that the interaction between 
the real particles and the zerons dissipates the energy among the 
many degrees of freedom of the zeron field, so that the whole of 
thermodynamics becomes a chaos. Weizel has not explained 
how he hopes to avoid this danger. 

The standpoint of the entire group of publications mentioned 
so far can perhaps best be defined by recalling a similar discus- 
sion of theory of special relativity. Anyone who was dis- 
satisfied with Einstein's negation of the ether, of absolute space 
and of absolute time could then argue as follows: The non- 
existence of absolute space and absolute time is by no means 
proved by the theory of special relativity. It has been shown 
only that true space and true time do not occur directly in any 
ordinary experiment; but if this aspect of the laws of nature 
has been correctly taken into account, and thus the correct 
'apparent' times have been introduced for moving co-ordinate 
systems, there would be no arguments against the assumption of 
an absolute space. It would even be plausible to assume that the 
centre of gravity of our galaxy is (at least approximately) at 
rest in absolute space. The critic of the special theory of rela- 
tivity might add that we may hope that future measurements 
will allow the unambiguous definition of absolute space (that is, 
of the 'hidden parameter' of the theory of relativity) and that 
the theory of relativity will thus be refuted. 



It is seen at once that this argument cannot be refuted by 
experiment, since it as yet makes no assertions which differ from 
those of the theory of special relativity. But such an interpreta- 
tion would destroy in the language used the decisive symmetry 
property of the theory, namely, the Lorentz invariance, and it 
must therefore be considered inappropriate. 

The analogy to quantum theory is obvious. The laws of quan- 
tum theory are such that the 'hidden parameters', invented ad 
hoc, can never be observed. The decisive symmetry properties 
are thus destroyed if we introduce the hidden parameters as a 
fictitious entity into the interpretation of the theory. 

The work of Blochinzev and Alexandrov is quite different in 
its statement of the problem from those discussed before. These 
authors expressly and from the beginning restrict their objections 
against the Copenhagen interpretation to the philosophical side 
of the problem. The physics of this interpretation is accepted un- j 

The external form of the polemic, however, is so much the 
sharper: 'Among the different idealistic trends in contemporary 
physics the so-called Copenhagen school is the most reactionary. 
The present article is devoted to the unmasking of the idealistic 
and agnostic speculations of this school on the basic problems 
of quantum physics,' writes Blochinzev in his introduction. The 
acerbity of the polemic shows that here we have to do not with 
science alone but with a confession of faith, with adherence to 
a certain creed. The aim is expressed at the end with a quotation 
from the work of Lenin: 'However marvellous, from the point 
of view of the common human intellect, the transformation of 
the unweighable ether into weighable material, however strange 
the electrons lack of any but electromagnetic mass, however 
unusual the restriction of the mechanical laws of motion to but 
one realm of natural phenomena and their subordination to the 
deeper laws of electromagnetic phenomena, and so on — all this j 
is but another confirmation of dialectic materialism.' This latter 
statement seems to make Blochinzev's discussion about the rela- 
tion of quantum theory to the philosophy of dialectic material- 
ism less interesting in so far as it seems to degrade it to a staged 
trial in which the verdict is known before the trial has begun. 
Still it is important to get complete clarity about the arguments 


brought forward by Blochinzev and Alexandrov. 

Here, where the task is to rescue materialistic ontology, the 
attack is chiefly made against the introduction of the observer 
into the interpretation of quantum theory. Alexandrov writes: 
'We must therefore understand by "result of measurement" in 
quantum theory only the objective effect of the interaction of 
the electron with a suitable object. Mention of the observer must 
be avoided, and we must treat objective conditions and objective 
effects. A physical quantity is an objective characteristic of the 
phenomenon, but not the result of an observation.' According 
to Alexandrov, the wave function in configuration space charac- 
terizes the objective state of the electron. • 

In his presentation Alexandrov overlooks the fact that the 
formalism of quantum theory does not allow the same degree of 
objectivation as that of classical physics. For instance, if the 
interaction of a system with the measuring apparatus is treated 
as a whole according to quantum mechanics and if both are 
regarded as cut off from the rest of the world, then the formalism 
of quantum theory does not as a rule lead to a definite result; 
it will not lead, e.g., to the blackening of the photographic plate 
at a given point. If one tries to rescue Alexandrov's 'objective 
effect' by saying that 'in reality' the plate is blackened at a 
given point after the interaction, the rejoinder is that the quan- 
um mechanical treatment of the closed system consisting of 
electron, measuring apparatus and plate is no longer being 
applied. It is the 'factual' character of an event describable in 
terms of the concepts of daily life which is not without further 
comment contained in the mathematical formalism of quantum 
theory, and which appears in the Copenhagen interpretation by 
the introduction of the observer. Of course the introduction of 
the observer must not be misunderstood to imply that some kind 
of subjective features are to be brought into the description of 
nature. The observer has, rather, only the function of registering 
decisions, i.e., processes in space and time, and it does not matter 
whether the observer is an apparatus or a human being; but the 
registration, i.e., the transition from the 'possible' to the 
'actual', is absolutely necessary here and cannot be omitted 
from the interpretation of quantum theory. At this point quan- 
tum theory is intrinsically connected with thermodynamics in so 



far as every act of observation is by its very nature an irre-| 
versible process; it is only through such irreversible processes 
that the formalism of quantum theory can be consistently con- 
nected with actual events in space and time. Again the irreversi- f 
bility is — when projected into the mathematical representation " 
of the phenomena — a consequence of the observer's incomplete 
knowledge of the system and in so far not completely 'ob- 

Blochinzev formulates matter slightly differently from Alex- 
androv: 'In quantum mechanics we describe not a state of the 
particle in itself but the fact that the particle belongs to this or 
that statistical assembly. This belonging is completely objective 
and does not depend on statements made by the observer.' Such 
formulations, however, take us very far — probably too far — 
away from materialistic ontology. To make this point clear it 
is useful to recall how this belonging to a statistical assembly is 
used in the interpretation of classical thermodynamics. If an* 
observer has determined the temperature of a system and wants 
to draw from his results conclusions about the molecular motion? 
in the system he is able to say that the system is just one sample! 
out of a canonical ensemble and thus he may consider it as pos*| 
sibly having different energies. 'In reality' — so we would con^ 
elude in classical physics — the system has only one definite* 
energy at a given time, and none of the others is realized. The ob| 
server has been deceived if he considered a different energy at 
that moment as possible. The canonical ensemble contains state- 
ments not only about the system itself but also about the 
observer's incomplete knowledge of the system. If Blochinzev itt 
quantum theory tries to call a system's belonging to an assembly 
'completely objective', he used the word 'objective' in a different 
sense from that in classical physics. For in classical physics this 
belonging means, as has been said, statements not only about the 
system but also about the observer's degree of knowledge of the 
system. One exception must be made to this assertion in quan- 
tum theory. If in quantum theory the assembly is characterized 
by only one wave function in configuration space (and not, as 
usual, by a statistical matrix), we meet a special situation (the 
so-called 'pure case') in which the description can be called 
objective in some sense and in which the element of incomplete 


knowledge does not occur immediately. But since every measure- 
ment would (on account of its irreversible features) reintroduce 
the element of incomplete knowledge, the situation would not 
be fundamentally different. 

' Above all, we see from these formulations how difficult it is 
when we try to push new ideas into an old system of concepts 
belonging to an earlier philosophy — or, to use an old metaphor, 
when we attempt to put new wine into old bottles. Such at- 
tempts are always distressing, for they mislead us into con- 
tinually occupying ourselves with the inevitable cracks in the 
old bottles instead of rejoicing over the new wine. We cannot 
possibly expect those thinkers who a century ago introduced 
dialectic materialism to have foreseen the development of 
quantum theory. Their concepts of matter and reality could not 
possibly be adapted to the results of the refined experimental 
technique of our days. 

Perhaps one should add at this point some general remarks 
about the attitude of the scientist to a special creed; it may be a 
religious or a political creed. The fundamental difference be- 
tween the religious and the political creed — that the latter refers 
to the immediate material reality of the world around us, while 
the former has as its object another reality beyond the material 
world — is not important for this special question; it is the prob- 
lem of creed itself that is to be discussed. From what has been 
said one would be inclined to demand that the scientist should 
never rely on special doctrines, never confine his method of 
thinking to a special philosophy. He should always be prepared 
to have the foundations of his knowledge changed by new ex- 
perience. But this demand would again be an oversimplification 
of our situation in life for two reasons. The first is that the 
structure of our thinking is determined in our youth by ideas 
which we meet at that time or by getting into contact with 
strong personalities from whom we learn. This structure will 
form an integrating part of all our later work and it may well 
make it difficult for us to adapt ourselves to entirely different 
ideas later on. The second reason is that we belong to a com- 
munity or a society. This community is kept together by com- 
mon ideas, by a common scale of ethical values, or by a common 
language in which one speaks about the general problems of life. 



The common ideas may be supported by the authonty of 

church, a party or the state and, even if this is not the case, it 

may be difficult to go away from the common ideas without get! 

ting into conflict with the community. Yet the results of scientific 5 

thinking may contradict some of the common ideas. Certainly 

it would be unwise to demand that the scientist should generally 

not be a loyal member of his community, that he should be de 

prived of the happiness that may come from belonging to ; 

community, and it would be equally unwise to desire that th^ 

common ideas of society which from the scientific point of viey 

are always simplifications should change instantaneously wit 

the progress of scientific knowledge, that they should be « 

variable as scientific theories must necessarily be. Therefore, af 

this point we come back even in our time to the old problem of 

the 'twofold truth' that has filled the history of Christian re 1 

ligion throughout the later Middle Ages. There is the very dis 

putable doctrine that 'positive religion— whatever form it maj 

take _j s an indispensable need for the mass of the people, whil^ 

the man of science seeks the real truth back of religion and seek' 

it only there.' 'Science is esoteric,' so it is said, 'it is only fc 

the few.' If in our time political doctrines and social activitie 

take the part of positive religion in some countries, the problem] 

still essentially the same. The scientist's first claim will always r 

intellectual honesty, while the community will frequently ask < 

the scientist that— in view of the invariability of science— he ; 

least wait a few decades before expressing in public his dissent 

ing opinions. There is probably no simple solution to this proti 

lem, if tolerance alone is not sufficient; but some consolatioj 

may come from the fact that it is certainly an old problem 

longing to human life. 

Coming back now to the counterproposals to the Copenhagei 
interpretation of quantum theory we have to discuss the second 
group of proposals, which try to change quantum theory is 
order to arrive at a different philosophical interpretation. Thj 
most careful attempt in this direction has been made by Janossy* 
who has realized that the rigorous validity of quantum me 
chanics compels us to depart from the reality concept of classics 
physics. He therefore seeks to alter quantum mechanics in sucflj 
a way that, although many of the results remain true, its strut* 


ture approaches that of classical physics. His point of attack is 
what is called 'the reduction of wave packets', i.e., the fact that 
the wave function or, more generally, the probability function 
changes discontinuously when the observer takes cognizance of 
a result of measurement. Janossy notices that this reduction can- 
not be deduced from the differential equations of the mathe- 
matical formalism and he believes that he can conclude from 
this that there is an inconsistency in the usual interpretation. It 
is well known that the 'reduction of wave packets' always 
appears in the Copenhagen interpretation when the transition 
is completed from the possible to the actual. The probability 
function, which covered a wide range of possibilities, is suddenly 
reduced to a much narrower range by the fact that the experi- 
ment has led to a definite result, that actually a certain event 
has happened. In the formalism this reduction requires that the 
so-called interference of probabilities, which is the most char- 
acteristic phenomena of quantum theory, is destroyed by the 
partly undefinable and irreversible interactions of the system 
with the measuring apparatus and the rest of the world. Janossy 
now tries to alter quantum mechanics by the introduction of so- 
called damping terms into the equations, in such a way that the 
interference terms disappear of themselves after a finite time. 
Even if this corresponds to reality— and there is no reason to 
suppose this from the experiments that have been performed — 
there would still remain a number of alarming consequences of 
such an interpretation, as Janossy himself points out (e.g., waves 
which are propagated faster than the velocity of light, inter- 
change of the time sequence of cause and effect, etc.) . There- 
fore, we should hardly be ready to sacrifice the simplicity of 
quantum theory for this kind of view until we are compelled by 
experiments to do so. 

Among the remaining opponents of what is sometimes called 
the 'orthodox' interpretation of quantum theory, Schrodinger 
has taken an exceptional position inasmuch as he would ascribe 
the 'objective reality' not to the particles but to the waves and 
is not prepared to interpret the waves as 'probability waves 
only'. In his paper entitled 'Are There Quantum Jumps?' he 
attempts to deny the existence of quantum jumps altogether (one 
may question the suitability of the term 'quantum jump' at this 



place and could replace it by the less provocative term 'dis- 
continuity'). Now, Schrodinger 's work first of all contains some 
misunderstanding of the usual interpretation. He overlooks 
the fact that only the waves in configuration space (or the 
'transformation matrices') are probability waves in the usual in- 
terpretation, while the three-dimensional matter waves or radia- 
tion waves are not. The latter have just as much and just as 
little 'reality' as the particles; they have no direct connection 
with probability waves but have a continuous density of energy 
and momentum, like an electromagnetic field in Maxwell's 
theory. Schrodinger therefore rightly emphasizes that at this 
point the processes can be conceived of as being more continuous 
than they usually are. But this interpretation cannot remove the 
element of discontinuity that is found everywhere in atomic 
physics; any scintillation screen or Geiger counter demonstrates 
this element at once. In the usual interpretation of quantum 
theory it is contained in the transition from the possible to the 
actual. Schrodinger himself makes no counterproposal as to how 
he intends to introduce the element of discontinuity, everywhere 
observable, in a different manner from the usual interpretation. 
Finally, the criticism which Einstein, Laue and others have 
expressed in several papers concentrates on the question whether 
the Copenhagen interpretation permits a unique, objective de- 
scription of the physical facts. Their essential arguments may be 
stated in the following terms 1 : The mathematical scheme of 
quantum theory seems to be a perfectly adequate description of 
the statistics of atomic phenomena. But even if its statements 
about the probability of atomic events are completely correct, 
this interpretation does not describe what actually happens inde- 
pendently of or between the observations. But something must 
happen, this we cannot doubt; this something need not be de- 
scribed in terms of electrons or waves or light quanta, but unless 
it is described somehow the task of physics is not completed. It 
cannot be admitted that it refers to the act of observation only. 
The physicist must postulate in his science that he is studying a 
world which he himself has not made and which would be 
present, essentially unchanged, if he were not there. Therefore, 
the Copenhagen interpretation offers no real understanding of 
the atomic phenomena. 


It is easily seen that what this criticism demands is again the 
old materialistic ontology. But what can be the answer from the 
point of view of the Copenhagen interpretation? 

We can say that physics is a part of science and as such aims 
at a description and understanding of nature. Any kind of 
understanding, scientific or not, depends on our language, on 
the communication of ideas. Every description of phenomena, 
of experiments and their results, rests upon language as the only 
means of communication. The words of this language represent 
the concepts of daily life, which in the scientific language of 
physics may be refined to the concepts of classical physics. These 
concepts are the only tools for an unambiguous communication 
about events, about the setting up of experiments and about 
their results. If therefore the atomic physicist is asked to give 
a description of what really happens in his experiments, the 
words 'description' and 'really' and 'happens' can only refer to 
the concepts of daily life or of classical physics. As soon as 
the physicist gave up this basis he would lose the means of 
unambiguous communication and could not continue in his 
science. Therefore, any statement about what has 'actually 
happened' is a statement in terms of the classical concepts and 
— because of thermodynamics and of the uncertainty relations — 
by its very nature incomplete with respect to the details of the 
atomic events involved. The demand to 'describe what hap- 
pens' in the quantum-theoretical process between two successive 
observations is a contradiction in adjecto, since the word 'de- 
scribe' refers to the use of the classical concepts, while these 
concepts cannot be applied in the space between the observa- 
tions; they can only be applied at the points of observation. 

It should be noticed at this point that the Copenhagen in- 
terpretation of quantum theory is in no way positivistic. For, 
whereas positivism is based on the sensual perceptions of 
the observer as the elements of reality, the Copenhagen inter- 
pretation regards things and processes which are describable in 
terms of classical concepts, i.e., the actual, as the foundation of 
any physical interpretation. 

At the same time we see that the statistical nature of the laws 
of microscopic physics cannot be avoided, since any knowledge 
of the 'actual' is — because of the quantum-theoretical laws — 



by its very nature an incomplete knowledge. 

The ontology of materialism rested upon the illusion that the 
kind of existence, the direct 'actuality' of the world around us, 
can be extrapolated into the atomic range. This extrapolation is 
impossible, however. 

A few remarks may be added concerning the formal structure 
of all the counterproposals hitherto made against the Copen- 
hagen interpretation of quantum theory. All these proposals 
have found themselves compelled to sacrifice the essential sym- 
metry properties of quantum theory (for instance, the symmetry 
between waves and particles or between position and velocity). 
Therefore, we may well suppose that the Copenhagen interpreta- 
tion cannot be avoided if these symmetry properties — like the 
Lorentz invariance in the theory of relativity — are held to be a 
genuine feature of nature; and every experiment yet performed 
supports this view. 

Quantum Theory and the Structure of 


THE concept of matter has undergone a great number of 
changes in the history of human thinking. Different interpreta- 
tions have been given in different philosophical systems. All 
these different meanings of the word are still present in a greater 
or lesser degree in what we conceive in our time as the word 

The early Greek philosophy from Thales to the Atomists, in 
seeking the unifying principle in the universal mutability of all 
things, had formed the concept of cosmic matter, a world sub- 
stance which experiences all these transformations, from which 
all individual things arise and into which they become again 
transformed. This matter was partly identified with some spe- 
cific matter like water or air or fire; only partly, because it had 
no other attribute but to be the material from which all things' 
are made. 

Later, in the philosophy of Aristotle, matter was thought of in 
the relation between form and matter. All that we perceive in 
the world of phenomena around us is formed matter. Matter is 
in itself not a reality but only a possibility, a 'potentia'; it exists 
only by means of form. In the natural process the 'essence', 
as Aristotle calls it, passes over from mere possibility through 
form into actuality. The matter of Aristotle is certainly not a 
specific matter like water or air, nor is it simply empty space; it 
is a kind of indefinite corporeal substratum, embodying the pos- 
sibility of passing over into actuality by means of the form. The 
typical examples of this relation between matter and form in the 
philosophy of Aristotle are the biological processes in which 



matter is formed to become the living organism, and the build- 
ing and forming activity of man. The statue is potentially in the 
marble before it is cut out by the sculptor. 

Then, much later, starting from the philosophy of Descartes, 
matter was primarily thought of as opposed to mind. There were 
the two complementary aspects of the world, 'matter' and 
'mind', or, as Descartes put it, the 'res extensa' and the 'res 
cogitans'. Since the new methodical principle of natural 
science, especially of mechanics, excluded all tracing of corporeal 
phenomena back to spiritual forces, matter could be considered 
as a reality of its own independent of the mind and of any super- 
natural powers. The 'matter' of this period is 'formed matter', 
the process of formation being interpreted as a causal chain of 
mechanical interactions; it has lost its connection with vege- 
tative soul of Aristotelian philosophy, and therefore the dualism 
between matter and form is no longer relevant. It is this concept 
of matter which constitutes by far the strongest component in 
our present use of the word 'matter'. 

Finally, in the natural science of the nineteenth century an- 
other dualism has played some role, the dualism between matter 
and force. Matter is that on which forces can act; or matter can 
produce forces. Matter, for instance, produces the force of 
gravity, and this force acts on matter. Matter and force are two 
distinctly different aspects of the corporeal world. In so far as 
the forces may be formative forces this distinction comes closer 
to the Aristotelian distinction of matter and form. On the other 
hand, in the most recent development of modern physics this 
distinction between matter and force is completely lost, since 
every field of force contains energy and in so far constitutes 
matter. To every field of force there belongs a specific kind of 
elementary particles with essentially the same properties as all 
other atomic units of matter. 

When natural science investigates the problem of matter it 
can do so only through a study of the forms of matter. The 
infinite variety and mutability of the forms of matter must be 
the immediate object of the investigation and the efforts must be 
directed toward finding some natural laws, some unifying prin- 
ciples that can serve as a guide through this immense field. 
Therefore, natural science— and especially physics— has concen- 


trated its interest for a long period on an analysis of the structure 
of matter and of the forces responsible for this structure. 

Since the time of Galileo the fundamental method of natural 
science had been the experiment. This method made it possible 
to pass from general experience to specific experience, to single 
out characteristic events in nature from which its 'laws' could 
be studied more directly than from general experience. If one 
wanted to study the structure of matter one had to do experi- 
ments with matter. One had to expose matter to extreme condi- 
tions in order to study its transmutations there, in the hope of 
finding the fundamental features of matter which persist under 
all apparent changes. 

In the early days of modern natural science this was the object 
of chemistry, and this endeavour led rather early to the concept 
of the chemical element. A substance that could not be further 
dissolved or disintegrated by any of the means at the disposal of 
the chemist — boiling, burning, dissolving, mixing with other 
substances, etc. — was called an element. The introduction of this 
concept was a first and most important step toward an under 
standing of the structure of matter. The enormous variety of 
substances was at least reduced to a comparatively small number 
of more fundamental substances, the 'elements', and thereby 
some order could be established among the various phenomena 
of chemistry. The word 'atom' was consequently used to desig- 
nate the smallest unit of matter belonging to a chemical element, 
and the smallest particle of a chemical compound could be pic- 
tured as a small group of different atoms. The smallest particle 
of the element iron, e.g., was an iron atom, and the smallest 
particle of water, the water molecule, consisted of one oxygen 
atom and two hydrogen atoms. 

The next and almost equally important step was the discovery 
of the conservation of mass in the chemical process. For instance, 
when the element carbon is burned into carbon dioxide the mass 
of the carbon dioxide is equal to the sum of the masses of the 
carbon and the oxygen before the process. It was this discovery 
that gave a quantitative meaning to the concept of matter: inde- 
pendent of its chemical properties matter could be measured by 
its mass. 
During the following period, mainly the nineteenth century, 




a number of new chemical elements were discovered; in our 
time this number has reached one hundred. This development 
showed quite clearly that the concept of the chemical element 
had not yet reached the point where one could understand the 
unity of matter. It was not satisfactory to believe that there are 
very many kinds of matter, qualitatively different and without 
any connection between one another. 

In the beginning of the nineteenth century some evidence for 
a connection between the different elements was found in the 
fact that the atomic weights of different elements frequently 
seemed to be integer multiples of a smallest unit near to the 
atomic weight of hydrogen. The similarity in the chemical be- 
haviour of some elements was another hint leading in the same 
direction. But only the discovery of forces much stronger than j 
those applied in chemical processes could really establish the con- 
nection between the different elements and thereby lead to a 
closer unification of matter. 

These forces were actually found in the radioactive process 
discovered in 1896 by Becquerel. Successive investigations by 
Curie, Rutherford and others revealed the transmutation of 
elements in the radioactive process. The a-particles are emitted 
in these processes as fragments of the atoms with an energy 
about a million times greater than the energy of a single atomic 
particle in a chemical process. Therefore, these particles could 
be used as new tools for investigating the inner structure of the 
atom. The result of Rutherford's experiments on the scattering 
of a-rays was the nuclear model of the atom in 191 1. The most 
important feature of this well-known model was the separation 
of the atom into two distinctly different parts, the atomic nucleus 
and the surrounding electronic shells. The nucleus in the middle 
of the atom occupies only an extremely small fraction of the 
space filled by the atom (its radius is about a hundred thousand 
times smaller than that of the atom), but contains almost its 
entire mass. Its positive electric charge, which is an integer 
multiple of the so-called elementary charge, determines the num- 
ber of the surrounding electrons — the atom as a whole must be 
electrically neutral — and the shapes of their orbits. 

This distinction between the atomic nucleus and the electronic 
shells at once gave a proper explanation of the fact that for 


chemistry the chemical elements are the last units of matter and 
that very much stronger forces are required to change the ele- 
ments into each other. The chemical bond between neighbouring 
atoms is due to an interaction of the electronic shells, and the 
energies of this interaction are comparatively small. An electron 
that is accelerated in a discharge tube by a potential of only 
several volts has sufficient energy to excite the electronic shells 
to the emission of radiation, or to destroy the chemical bond in 
a molecule. But the chemical behaviour of the atom, though it 
consists of the behaviour of its electronic shells, is determined by 
the charge of the nucleus. One has to change the nucleus if one 
wants to change the chemical properties, and this requires 
energies about a million times greater. 

The nuclear model of the atom, however, if it is thought of as 
a system obeying Newton's mechanics, could not explain the 
stability of the atom. As has been pointed out in an earlier 
chapter, only the application of quantum theory to this model 
through the work of Bohr could account for the fact that, for 
example, a carbon atom after having been in interaction with 
other atoms or after having emitted radiation always finally 
remains a carbon atom with the same electronic shells as before. 
This stability could be explained simply by those features of 
quantum theory that prevent a simple objective description in 
space and time of the structure of the atom. 

In this way one finally had a first basis for the understanding 
of matter. The chemical and other properties of the atoms could 
be accounted for by applying the mathematical scheme of 
quantum theory to the electronic shells. From this basis one 
could try to extend the analysis of the structure of matter in two 
opposite directions. One could either study the interaction of 
atoms, their relation to larger units like molecules or crystals 
or biological objects; or one could try through the investigation 
of the atomic nucleus and its components to penetrate to the 
final unity of matter. Research has proceeded on both lines dur- 
ing the past decades and we shall in the following pages be con- 
cerned with the role of quantum theory in these two fields. 

The forces between neighbouring atoms are primarily electric 
forces, the attraction of opposite and the repulsion of equal 
charges; the electrons are attracted by the nuclei and repelled 



from each other. But these forces act not according to the laws 
of Newtonian mechanics but those of quantum mechanics. 

This leads to two different types of binding between atoms. In 
the one type the electron of one atom passes over to the other 
one, for example, to fill up a nearly closed electronic shell. In 
this case both atoms are finally charged and form what the 
physicist calls ions, and since their charges are opposite they 
attract each other. 

In the second type one electron belongs in a way characteristic 
of quantum theory to both atoms. Using the picture of the elec- 
tronic orbit, one might say that the electron goes around both 
nuclei spending a comparable amount of time in the one and in 
the other atom. This second type of binding corresponds to what 
the chemists call a valency bond. 

These two types of forces, which may occur in any mixture, 
cause the formation of various groupings of atoms and seem to 
be ultimately responsible for all the complicated structures of 
matter in bulk that are studied in physics and chemistry. The 
formation of chemical compounds takes place through the 
formation of small closed groups of different atoms, each group 
being one molecule of the compound. The formation of crystals 
is due to the arrangement of the atoms in regular lattices. Metals 
are formed when the atoms are so tightly packed that their outer 
electrons can leave their shells and wander through the whole 
crystal. Magnetism is due to the spinning motion of the electron, 
and so on. 

In all these cases the dualism between matter and force can 
still be retained, since one may consider nuclei and electrons as 
the fragments of matter that are kept together by means of the 
electromagnetic forces. 

While in this way physics and chemistry have come to an 
almost complete union in their relations to the structure of 
matter, biology deals with structures of a more complicated and 
somewhat different type. It is true that in spite of the wholeness 
of the living organism a sharp distinction between animate and 
inanimate matter can certainly not be made. The development 
of biology has supplied us with a great number of examples 
where one can see that specific biological functions are carried 
by special large molecules or group or chains of such molecules, 


and there has been an increasing tendency in modern biology to 
explain biological processes as consequences of the laws of 
physics and chemistry. But the kind of stability that is displayed 
by the living organism is of a nature somewhat different from 
the stability of atoms or crystals. It is a stability of process or 
function rather than a stability of form. There can be no doubt 
that the laws of quantum theory play a very important role in 
the biological phenomena. For instance, those specific quantum- 
theoretical forces that can be described only inaccurately by the 
concept of chemical valency are essential for the understanding 
of the big organic molecules and their various geometrical pat- 
terns; the experiments on biological mutations produced by 
radiation show both the relevance of the statistical quantum- 
theoretical laws and the existence of amplyfying mechanisms. 
The close analogy between the working of our nervous system 
and the functioning of modern electronic computers stresses 
again the importance of single elementary processes in the living 
organism. Still all this does not prove that physics and chemistry 
will, together with the concept of evolution, someday offer a 
complete description of the living organism. The biological pro- 
cesses must be handled by the experimenting scientist with 
greater caution than processes of physics and chemistry. As Bohr 
has pointed out, it may well be that a description of the living 
organism that could be called complete from the standpoint of 
the physicist cannot be given, since it would require experiments 
that interfere too strongly with the biological functions. Bohr has 
described this situation by saying that in biology we are con- 
cerned with manifestations of possibilities in that nature to 
which we belong rather than with outcomes of experiments 
which we can ourselves perform. The situation of complemen- 
tarity to which this formulation alludes is represented as a ten- 
dency in the methods of modern biological research which, on 
the one hand, makes full use of all the methods and results of 
physics and chemistry and, on the other hand, is based on con- 
cepts referring to those features of organic nature that are not 
contained in physics or chemistry, like the concept of life itself. 
So far we have followed the analysis of the structure of matter 
in one direction: from the atom to the more complicated struc- 
tures consisting of many atoms; from atomic physics to the 


physics of solid bodies, to chemistry and to biology. Now we 
have to turn to the opposite direction and follow the line of 
research from the outer parts of the atom to the inner parts and 
from the nucleus to the elementary particles. It is this line which 
will possibly lead to an understanding of the unity of matter. 
Here we need not be afraid of destroying characteristic struc- 
tures by our experiments. When the task is set to test the final 
unity of matter we may expose matter to the strongest possible 
forces, to the most extreme conditions, in order to see whether 
any matter can ultimately be transmuted into any other matter. 

The first step in this direction was the experimental analysis 
of the atomic nucleus. In the initial period of these studies, 
which filled approximately the first three decades of our century, 
the only tools available for experiments on the nucleus were the 
a-particles emitted from radioactive bodies. With the help of 
these particles Rutherford succeeded in 1919 in transmuting 
nuclei of light elements; he could, for instance, transmute a 
nitrogen nucleus into an oxygen nucleus by adding the a-particle 
to the nitrogen nucleus and at the same time knocking out one 
proton. This was the first example of processes on a nuclear 
scale that reminded one of chemical processes, but led to the 
artificial transmutation of elements. The next substantial prog- 
ress was, as is well known, the artificial acceleration of protons 
by means of high-tension equipment to energies sufficient to 
cause nuclear transmutation. Voltages of roughly one million 
volts are required for this purpose and Cockcroft and Walton in 
their first decisive experiment succeeded in transmuting nuclei 
of the element lithium into those of helium. This discovery 
opened up an entirely new line of research, which may be called 
nuclear physics in the proper sense and which very soon led to a 
qualitative understanding of the structure of the atomic nucleus. 

The structure of the nucleus was indeed very simple. The 
atomic nucleus consists of only two kinds of elementary par- 
ticles. The one is the proton which is at the same time simply the 
hydrogen nucleus; the other is called neutron, a particle which 
has roughly the mass of the proton but is electrically neutral. 
Every nucleus can be characterized by the number of protons 
and neutrons of which it consists. The normal carbon nucleus, 
for instance, consists of 6 protons and 6 neutrons. There are 


other carbon nuclei, less frequent in number (called isotopic to 
the first ones), that consist of 6 protons and 7 neutrons, etc. So 
one had finally reached a description of matter in which, instead 
of the many different chemical elements, only three fundamental 
units occurred: the proton, the neutron and the electron. All 
matter consists of atoms and therefore is constructed from these 
three fundamental building stones. This was not yet the unity 
of matter, but certainly a great step toward unification and — 
perhaps still more important — simplification. There was of 
course still a long way to go from the knowledge of the two 
building stones of the nucleus to a complete understanding of its- 
structure. The problem here was somewhat different from the 
corresponding problem in the outer atomic shells that had been 
solved in the middle of the twenties. In the electronic shells the 
forces between the particles were known with great accuracy, 
but the dynamic laws had to be found, and were found in 
quantum mechanics. In the nucleus the dynamic laws could 
well be supposed to be just those of quantum mechanics, but the 
forces between the particles were not known beforehand; they 
had to be derived from the experimental properties of the nuclei. 
This problem has not yet been completely solved. The forces 
have probably not such a simple form as the electrostatic forces 
in the electronic shells and therefore the mathematical difficulty 
of computing the properties from complicated forces and the 
inaccuracy of the experiments make progress difficult. But a 
qualitative understanding of the structure of the nucleus has 
definitely been reached. 

Then there remained the final problem, the unity of matter. 
Are these fundamental building stones — proton, neutron and 
electron — final indestructible units of matter, atoms in the sense 
of Democritus, without any relation except for the forces that 
act between them or are they just different forms of the same 
kind of matter? Can they again be transmuted into each other 
and possibly into other forms of matter as well? An experimental 
attack on this problem requires forces and energies concentrated 
on atomic particles much larger than those that have been neces- 
sary to investigate the atomic nucleus. Since the energies stored 
up in atomic nuclei are not big enough to provide us with a tool 
for such experiments, the physicists have to rely either on the 


forces in cosmic dimensions or on the ingenuity and skill of the 

Actually, progress has been made on both lines. In the first 
case the physicists make use of the so-called cosmic radiation.. 
The electromagnetic fields on the surface of stars extending over 
huge spaces are under certain circumstances able to accelerate 
charged atomic particles, electrons and nuclei. The nuclei, owing 
to their greater inertia, seem to have a better chance of remain- 
ing in the accelerating field for a long distance, and finally when 
they leave the surface of the star into empty space they have 
already travelled through potentials of several thousand million 
volts. There may be a further acceleration in the magnetic fields 
between the stars; in any case the nuclei seem to be kept within 
the space of the galaxy for a long time by varying magnetic ij 
fields, and finally they fill this space with what one calls cosmic 
radiation. This radiation reaches the earth from the outside and 
consists of nuclei of practically all kinds, hydrogen and helium 
and many heavier elements, having energies from roughly a 
hundred or a thousand million electron volts to, again in rare j 
cases, a million times this amount. When the particles of this 
cosmic radiation penetrate into the atmosphere of the earth they 
hit the nitrogen atoms or oxygen atoms of the atmosphere or 
may hit the atoms in any experimental equipment exposed to the 

The other line of research was the construction of big ac-j 
celerating machines, the prototype of which was the so-called 
cyclitron constructed by Lawrence in California in the early 
thirties. The underlying idea of these machines is to keep by 
means of a big magnetic field the charged particles going round 
in circles a great number of times so that they can be pushed; 
again and again by electric fields on their way around. Machines 
reaching up to energies of several hundred million electron volts 
are in use in Great Britain, and through the co-operation of 
twelve European countries a very big machine of this type is 
now being constructed in Geneva which we hope will reach up 
to energies of 25,000 million electron volts. The experiments car-| 
ried out by means of cosmic radiation or of the big accelerators 
have revealed new interesting features of matter. Besides the! 
three fundamental building stones of matter — electron, proton j 



and neutron — new elementary particles have been found which 
can be created in these processes of highest energies and disap- 
pear again after a short time. The new particles have similar 
properties as the old ones except for their instability. Even the 
most stable ones have lifetimes of roughly only a millionth part 
of a second, and the lifetimes of others are even a thousand times 
smaller. At the present time about twenty-five different new 
elementary particles are known; the most recent one is the nega- 
tive proton. 

These results seem at first sight to lead away from the idea 
of the unity of matter, since the number of fundamental units of 
matter seems to have again increased to values comparable to 
the number of different chemical elements. But this would not 
be a proper interpretation. The experiments have at the same 
time shown that the particles can be created from other particles 
or simply from the kinetic energy of such particles, and they can 
again disintegrate into other particles. Actually the experiments 
have shown the complete mutability of matter. All the ele- 
mentary particles can, at sufficiently high energies, be trans- 
muted into other particles, or they can simply be created from 
kinetic energy and can be annihilated into energy, for instance, 
into radiation. Therefore, we have here actually the final proof 
for the unity of matter. All the elementary particles are made of 
the same substance, which we may call energy or universal 
matter; they are just different forms in which matter can appear. 

If we compare this situation with the Aristotelian concepts of 
matter and form, we can say that the matter of Aristotle, which 
is mere 'potentia', should be compared to our concept of energy, 
which gets into 'actuality' by means of the form, when the ele- 
mentary particle is created. 

Modern physics is of course not satisfied with only qualita- 
tive description of the fundamental structure of matter; it must 
try on the basis of careful experimental investigations to get a 
mathematical formulation of those natural laws that determine 
the 'forms' of matter, the elementary particles and their forces. 
A clear distinction between matter and force can no longer be 
made in this part of physics, since each elementary particle not 
only is producing some forces and is acted upon by forces, but it 
is at the same time representing a certain field of force. The 




quantum-theoretical dualism of waves and particles makes the ,',' 
same entity appear both as matter and as force. | 

All the attempts to find a mathematical description for the : 
laws concerning the elementary particles have so far started : 
from the quantum theory of wave fields. Theoretical work on ';' 
theories of this type started early in the thirties. But the very first 
investigations on this line revealed serious difficulties the roots of i 
which lay in the combination of quantum theory and the theory ; , 
of special relativity. At first sight it would seem that the two f 
theories, quantum theory and the theory of relativity, refer to | 
such different aspects of nature that they should have practically | 
nothing to do with each other, that it should be easy to fulfil the | 
requirements of both theories in the same formalism. A closer I 
inspection, however, shows that the two theories do interfere at I 
one point, and that it is from this point that all the difficulties | 

The theory of special relativity had revealed a structure of J 
space and time somewhat different from the structure that wasj 
generally assumed since Newtonian mechanics. The most char-1 
acteristic feature of this newly discovered structure is the ex-f 
istence of a maximum velocity that cannot be surpassed by anyf 
moving body or any travelling signal, the velocity of light. As al 
consequence of this, two events at distant points cannot have anyl 
immediate causal connection if they take place at such times thara 
a light signal starting at the instant of the event on one poinlf 
reaches the other point only after the time the other event haS 
happened there; and vice versa. In this case the two events may 
be called simultaneous. Since no action of any kind can reach 
from the one point, the two events are not connected by an)j 
from the one event at the one point in time to the other event at| 
the other point, the two events are not connected by any causa| 

For this reason any action at a distance of the type, say, 
the gravitational forces in Newtonian mechanics was not coml 
patible with the theory of special relativity. The theory had t<f 
replace such action by actions from point to point, from ora 
point only to the points in an infinitesimal neighbourhood. ThG 
most natural mathematical expressions for actions of this tyj 
were the differential equations for waves or fields that were ini 


variant for the Lorentz transformation. Such differential equa- 
tions exclude any direct action between 'simultaneous' events. 

Therefore, the structure of space and time expressed in the 
theory of special relativity implied an infinitely sharp boundary 
between the region of simultaneousness, in which no action 
could be transmitted, and the other regions, in which a direct 
action from event to event could take place. 

On the other hand, in quantum theory the uncertainty rela- 
tions put a definite limit on the accuracy with which positions 
and momenta, or time and energy, can be measured simul- 
taneously. Since an infinitely sharp boundary means an infinite 
accuracy with respect to position in space and time, the mo- 
menta or energies must be completely undetermined, or in fact 
arbitrarily high momenta and energies must occur with over- 
whelming probability. Therefore, any theory which tries to ful- 
fil the requirements of both special relativity and quantum 
theory will lead to mathematical inconsistencies, to divergencies 
in the region of very high energies and momenta. This sequence 
of conclusions may perhaps not seem strictly binding, since any 
formalism of the type under consideration is very complicated 
and could perhaps offer some mathematical possibilities for 
avoiding the clash between quantum theory and relativity. But 
so far all the mathematical schemes that have been tried did in 
fact lead either to divergencies, i.e., to mathematical contradic- 
tions, or did not fulfil all the requirements of the two theories. 
And it was easy to see that the difficulties actually came from the 
point that has been discussed. 

The way in which the convergent mathematical schemes did 
not fulfil the requirements of relativity or quantum theory was 
in itself quite interesting. For instance, one scheme, when in- 
terpreted in terms of actual events in space and time, led to a 
kind of time reversal; it would predict processes in which sud- 
denly at some point in space particles are created, the energy of 
which is later provided for by some other collision process be- 
tween elementary particles at some other point. The physicists 
are convinced from their experiments that processes of this type 
do not occur in nature, at least not if the two processes are 
separated by measurable distances in space and time. Another 
mathematical scheme tried to avoid the divergencies through a 



mathematical process which is called renormalization; it seemed 
possible to push the infinities to a place in the formalism where 
they could not interfere with the establishment of the well- 
defined relations between those quantities that can be directly 
observed. Actually this scheme has led to very substantial 
progress in quantum electrodynamics, since it accounts for some 
interesting details in the hydrogen spectrum that had not been 
understood before. A closer analysis of this mathematical 
scheme, however, has made it probable that those quantities 
which in normal quantum theory must be interpreted as proba- 
bilities can under certain circumstances become negative in the 
formalism of renormalization. This would prevent the consistent 
use of the formalism for the description of matter. 

The final solution of these difficulties has not yet been found. 
It will emerge someday from the collection of more and more 
accurate experimental material about the different elementary 
particles, their creation and annihilation, the forces between 
them. In looking for possible solutions of the difficulties one 
should perhaps remember that such processes with time reversal 
as have been discussed before could not be excluded experi- 
mentally, if they took place only within extremely small regions 
of space and time outside the range of our present experimental 
equipment. Of course one would be reluctant to accept such 
processes with time reversal if there could be at any later stage 
of physics the possibility of following experimentally such 
events in the same sense as one follows ordinary atomic events. 
But here the analysis of quantum theory and of relativity may 
again help us to see the problem in a new light. 

The theory of relativity is connected with a universal constant 
in nature, the velocity of light. This constant determines the 
relation between space and time and is therefore implicitly con- 
tained in any natural law which must fulfil the requirements of 
Lorentz invariance. Our natural language and the concepts of 
classical physics can apply only to phenomena for which the 
velocity of light can be considered as practically infinite. 

When we in our experiments approach the velocity of light 
we must be prepared for results which cannot be interpreted in 
these concepts. 

Quantum theory is connected with another universal constant 


of nature, Planck's quantum of action. An objective description 
for events in space and time is possible only when we have to 
deal with objects or processes on a comparatively large scale, 
where Planck's constant can be regarded as infinitely small. 
When our experiments approach the region where the quantum 
of action becomes essential we get into all those difficulties with 
the usual concepts that have been discussed in earlier chapters 
of this volume. 

There must exist a third universal constant in nature. This is 
obvious for purely dimensional reasons. The universal constants 
determine the scale of nature, the characteristic quantities that 
cannot be reduced to other quantities. One needs at least three 
fundamental units for a complete set of units. This is most easily 
seen from such conventions as the use of the c-g-s system (centi- 
metre, gram, second system) by the physicist. A unit of length 
one of time, and one of mass is sufficient to form a complete set; 
but one must have at least three units. One could also replace 
them by units of length, velocity and mass; or by units of length, 
velocity and energy, etc. But at least three fundamental units are 
necessary. Now, the velocity of light and Planck's constant of 
action provide only two of these units. There must be a third 
one, and only a theory which contains this third unit can possibly 
determine the masses and other properties of the elementary 
particles. Judging from our present knowledge of these particles 
the most appropriate way of introducing the third universal con- 
stant would be by the assumption of a universal length the value 
of which should be roughly io" 13 cm, that is, somewhat smaller 
than the radii of the light atomic nuclei. When from such three 
units one forms an expression which in its dimension corres- 
ponds to a mass, its value has the order of magnitude of the 
masses of the elementary particles. 

If we assume that the laws of nature do contain a third uni- 
versal constant of the dimension of a length and of the order of 
io" 13 cm, then we would again expect our usual concepts to 
apply only to regions in space and time that are large as com- 
pared to the universal constant. We should again be prepared 
for phenomena of a qualitatively new character when we in our 
experiments approach regions in space and time smaller than the 
nuclear radii. The phenomenon of time reversal, which has been 



discussed and which so far has only resulted from theoretical 
considerations as a mathematical possibility, might therefore 
belong to these smallest regions. If so, it could probably not be 
observed in a way that would permit a description in terms of 
the classical concepts. Such processes would probably, so far as 
they can be observed and described in classical terms, obey the 
usual time order. 

But all these problems will be a matter of future research in 
atomic physics. One may hope that the combined effort of ex- 
periments in the high energy region and of mathematical analy- 
sis will someday lead to a complete understanding of the unity of 
matter. The term 'complete understanding' would mean that 
the forms of matter in the sense of Aristotelian philosophy would 
appear as results, as solutions of a closed mathematical scheme 
representing the natural laws for matter. 


Language and Reality in Modern Physics 

THROUGHOUT the history of science new discoveries and 
new ideas have always caused scientific disputes, have led to 
polemical publications criticizing the new ideas, and such criti- 
cism has often been helpful in their development; but these con- 
troversies have never before reached that degree of violence 
which they attained after the discovery of the theory of relativity 
and in a lesser degree after quantum theory. In both cases the 
scientific problems have finally become connected with political 
issues, and some scientists have taken recourse to political 
methods to carry their views through. This violent reaction on 
the recent development of modern physics can only be under- 
stood when one realizes that here the foundations of physics have 
started moving; and that this motion has caused the feeling that 
the ground would be cut from science. At the same time it prob- 
ably means that one has not yet found the correct language with 
which to speak about the new situation and that the incorrect 
statements published here and there in the enthusiasm about the 
new discoveries have caused all kinds of misunderstanding. This 
is indeed a fundamental problem. The improved experimental 
technique of our time brings into the scope of science new as- 
pects of nature which cannot be described in terms of the com- 
mon concepts. But in what language, then, should they be 
described? The first language that emerges from the process of 
scientific clarification is in theoretical physics usually a mathe- 
matical language, the mathematical scheme, which allows one 
to predict the results of experiments. The physicist may be satis- 
fied when he has the mathematical scheme and knows how to 
use it for the interpretation of the experiments. But he has to 
speak about his results also to nonphysicists who will not be satis- 





fied unless some explanation is given in plain language, under- 
standable to anybody. Even for the physicist the description in 
plain language will be a criterion of the degree of understanding 
that has been reached. To what extent is such a description at 
all possible? Can one speak about the atom itself? This is a prob- 
lem of language as much as of physics, and therefore some 
remarks are necessary concerning language in general and scien- 
tific language specifically. 

Language was formed during the prehistoric age among the 
human race as a means for communication and as a basis for 
thinking. We know little about the various steps in its formation; 
but language now contains a great number of concepts which 
are a suitable tool for more or less unambiguous communication 
about events in daily life. These concepts are acquired gradually 
without critical analysis by using the language, and after having 
used a word sufficiently often we think that we more or less 
know what it means. It is of course a well-known fact that the 
words are not so clearly defined as they seem to be at first sight 
and that they have only a limited range of applicability. For 
instance, we can speak about a piece of iron or a piece of wood, 
but we cannot speak about a piece of water. The word 'piece' 
does not apply to liquid substances. Or, to mention another ex- 
ample: In discussions about the limitations of concepts, Bohr * 
likes to tell the following story: 'A little boy goes into a grocer's 
shop with a penny in his hand and asks: "Could I have a penny's 
worth of mixed sweets?" The grocer takes two sweets and hands 
them to the boy saying: "Here you have two sweets. You can do i 
the mixing yourself." ' A more serious example of the problema- 
tic relation between words and concepts is the fact that the words | 
'red' and 'green' are used even by people who are colourblind, '[ 
though the ranges of applicability of these terms must be quite 1; 
different for them from what they are for other people. 

This intrinsic uncertainty of the meaning of words was of f 
course recognized very early and has brought about the need fori 
definitions, or — as the word 'definition' says — for the setting ofl 
boundaries that determine where the word is to be used and^ 
where not. But definitions can be given only with the help of 
other concepts, and so one will finally have to rely on some con- 
cepts that are taken as they are, unanalyzed and undefined. 

In Greek philosophy the problem of the concepts in language 
has been a major theme since Socrates, whose life was — if we 
can follow Plato's artistic representation in his dialogues — a con- 
tinuous discussion about the content of the concepts in language 
and about the limitations in modes of expression. In order to 
obtain a solid basis for scientific thinking, Aristotle in his logic 
stared to analyze the forms of language, the formal structure of 
conclusions and deductions independent of their content. In this 
way he reached a degree of abstraction and precision that had 
been unknown up to that time in Greek philosophy and he 
thereby contributed immensely to the clarification, to the estab- 
lishment of order in our methods of thought. He actually created 
the basis for the scientific language. 

On the other hand, this logical analysis of language again 
involves the danger of an oversimplification. In logic the atten- 
tion is drawn to very special structures, unambiguous connec- 
tions between premises and deductions, simple patterns of 
reasoning, and all the other structures of language are neglected. 
These other structures may arise from associations between cer- 
tain meanings of words; for instance, a secondary meaning of a 
word which passes only vaguely through the mind when the 
word is heard may contribute essentially to the content of a 
sentence. The fact that every word may cause many only half- 
conscious movements in our mind can be used to represent some 
part of reality in the language much more clearly than by the 
use of the logical patterns. Therefore, the poets have often ob- 
jected to this emphasis in language and in thinking on the logical 
pattern, which — if I interpret their opinions correctly — can 
make language less suitable for its purpose. We may recall for 
instance the words in Goethe's Faust which Mephistopheles 
speaks to the young student (quoted from the translation by 
Anna Swanwick): 

Waste not your time, so fast it flies; 
Method will teach you time to win; 
Hence, my young friend, I would advise, 
With college logic to begin. 
Then will your mind be so well brac'd, 
In Spanish boots so tightly lac'd, 



That on 'twill circumspectly creep, 
Thought's beaten track securely keep, 
Nor will it, ignis-fatuus like, 
Into the path of error strike. 
Then many a day they'll teach you how 
The mind's spontaneous acts, till now 
As eating and as drinking free, 
Require a process; — one, two, three! 
In truth the subtle web of thought 
Is like the weaver's fabric wrought, 
One treadle moves a thousand lines, 
Swift dart the shuttles to and fro, 
Unseen the threads unnumber'd flow, 
A thousand knots one stroke combines. 
Then forward steps your sage to show, 
And prove to you it must be so; 
The first being so, and so the second, 
The third and fourth deduc'd we see; 
And if there were no first and second, 
Nor third nor fourth would ever be. 
This, scholars of all countries prize. 
Yet 'mong themselves no weavers rise. 
Who would describe and study aught alive. 
Seeks first the living spirit thence to drive: 
Then are the lifeless fragments in his hand, 
There only fails, alas! — the spirit-band. 

This passage contains an admirable description of the structure 
of language and of the narrowness of the simple logical patterns. 
On the other hand, science must be based upon language as 
the only means of communication and there, where the problem 
of unambiguity is of greatest importance, the logical patterns 
must play their role. The characteristic difficulty at this point 
may be described in the following way. In natural science we try 
to derive the particular from the general, to understand the par- 
ticular phenomenon as caused by simple general laws. The 
general laws when formulated in the language can contain only 
a few simple concepts — else the law would not be simple and 
general. From these concepts are derived an infinite variety of 



possible phenomena, not only qualitatively but with complete 
precision with respect to every detail. It is obvious that the con- 
cepts of ordinary language, inaccurate and only vaguely defined 
as they are, could never allow such derivations. When a chain 
of conclusions follows from given premises, the number of pos- 
sible links in the chain depends on the precision of the premises. 
Therefore, the concepts of the general laws must in natural 
science be defined with complete precision, and this can be 
achieved only by means of mathematical abstraction. 

In other sciences the situation may be somewhat similar in 
so far as rather precise definitions are also required; for instance, 
in law. But here the number of links in the chain of conclusions 
need not be very great, complete precision is not needed, and 
rather precise definitions in terms of ordinary language are suffi- 

In theoretical physics we try to understand groups of phe- 
nomena by introducing mathematical symbols that can be 
correlated with facts, namely, with the results of measurements. 
For the symbols we use names that visualize their correlation 
with the measurement. Thus the symbols are attached to the 
language. Then the symbols are interconnected by a rigorous 
system of definitions and axioms, and finally the natural laws are 
expressed as equations between the symbols. The infinite variety 
of solutions of these equations then corresponds to the infinite 
variety of particular phenomena that are possible in this part of 
nature. In this way the mathematical scheme represents the 
group of phenomena so far as the correlation between the sym- 
bols and the measurements goes. It is this correlation which per- 
mits the expression of natural laws in the terms of common 
language, since our experiments consisting of actions and ob- 
servations can always be described in ordinary language. 

Still, in the process of expansion of scientific knowledge the 
language also expands; new terms are introduced and the old 
ones are applied in a wider field or differently from ordinary 
language. Terms such as 'energy', 'electricity', 'entropy' are 
obvious examples. In this way we develop a scientific language 
which may be called a natural extension of ordinary language 
adapted to the added fields of scientific knowledge. 

During the past century a number of new concepts have been 




J $I 

introduced in physics, and in some cases it has taken consider- 
able time before the scientists have really grown accustomed to 
their use. The term 'electromagnetic field', for instance, which 
was to some extent already present in Faraday's work and which 
later formed the basis of Maxwell's theory, was not easily ac- 
cepted by the physicists, who directed their attention primarily 
to the mechanical motion of matter. The introducion of the 
concept really involved a change in scientific ideas as well, and 
such changes are not easily accomplished. 

Still, all the concepts introduced up to the end of the last 
century formed a perfectly consistent set applicable to a wide 
field of experience, and, together with the former concepts, 
formed a language which not only the scientists but also the 
technicians and engineers could successfully apply in their work. 
To the underlying fundamental ideas of this language belonged 
the assumptions that the order of events in time is entirely inde- 
pendent of their order in space, that Euclidean geometry is 
valid in real space, and that the events 'happen' in space and 
time independently of whether they are observed or not. It was 
not denied that every observation had some influence on the 
phenomenon to be observed but it was generally assumed that 
by doing the experiments cautiously this influence could be made 
arbitrarily small. This seemed in fact a necessary condition for 
the ideal of objectivity which was considered as the basis of all 
natural science. 

Into this rather peaceful state of physics broke quantum 
theory and the theory of special relativity as a sudden, at first 
slow and then gradually increasing, movement in the founda- 
tions of natural science. The first violent discussions developed 
around the problems of space and time raised by the theory of 
relativity. How should one speak about the new situation? 
Should one consider the Lorentz contradiction of moving bodies 
as a real contraction or only as an apparent contraction? Should 
one say that the structure of space and time was really different 
from what it had been assumed to be or should one only say that 
the experimental results could be connected mathematically in a 
way corresponding to this new structure, while space and time, 
being the universal and necessary mode in which things appear 
to us, remain what they had always been ? The real problem be- 

hind these many controversies was the fact that no language 
existed in which one could speak consistently about the new 
situation. The ordinary language was based upon the old con- 
cepts of space and time and this language offered the only 
unambiguous means of communication about the setting up and 
the results of the measurements. Yet the experiments showed 
that the old concepts could not be applied everywhere. 

The obvious starting point for the interpretation of the theory 
of relativity was therefore the fact that in the limiting case of 
small velocities (small compared with the velocity of light) the 
new theory was practically identical with the old one. Therefore, 
in this part of the theory it was obvious in which way the mathe- 
matical symbols had to be correlated with the measurements and 
with the terms of ordinary language; actually it was only 
through this correlation that the Lorentz transformation had 
been found. There was no ambiguity about the meaning of the 
words and the symbols in this region. In fact this correlation was 
already sufficient for the application of the theory to the whole 
field of experimental research connected with the problem of 
relativity. Therefore, the controversial questions about the 'real' 
or the 'apparent' Lorentz contradiction, or about the definition 
of the word 'simultaneous' etc., did not concern the facts but 
rather the language. 

With regard to the language, on the other hand, one has 
gradually recognized that one should perhaps not insist too 
much on certain principles. It is always difficult to find general 
convincing criteria for which terms should be used in the lan- 
guage and how they should be used. One should simply wait for 
the development of the language, which adjusts itself after some 
time to the new situation. Actually in the theory of special rela- 
tivity this adjustment has already taken place to a large extent 
during the past fifty years. The distinction between 'real' and 
'apparent' contraction, for instance, has simply disappeared. 
The word 'simultaneous' is used in line with the definition given 
by Einstein, while for the wider definition discussed in an earlier 
chapter the term 'at a space-like distance' is commonly used, etc. 

In the theory of general relativity the idea of a non-Euclidean 
geometry in real space was strongly contradicted by some phi- 
losophers who pointed out that our whole method of setting up 


the experiments already presupposed Euclidean geometry. 

In fact if a mechanic tries to prepare a perfectly plane surface, 
he can do it in the following way. He first prepares three surfaces 
of, roughly, the same size which are, roughly, plane. Then he 
tries to bring any two of the three surfaces into contact by put- 
ting them against each other in different relative positions. The 
degree to which this contact is possible on the whole surface is a 
measure of the degree of accuracy with which the surfaces can 
be called 'plane'. He will be satisfied with his three surfaces 
only if the contact between any two of them is complete every- 
where. If this happens one can prove mathematically that 
Euclidean geometry holds on the three surfaces. In this way, it 
was argued, Euclidean geometry is just made correct by our own 

From the point of view of general relativity, of course, one 
can answer that this argument proves the validity of Euclidean 
geometry only in small dimensions, in the dimensions of our ex- 
perimental equipment. The accuracy with which it holds in this 
region is so high that the above process for getting plane surfaces 
can always be carried out. The extremely slight deviations from 
Euclidean geometry which still exist in this region will not be 
realized since the surfaces are made of material which is not 
strictly rigid but allows for very small deformations and since 
the concept of 'contact' cannot be defined with complete pre- 
cision. For surfaces on a cosmic scale the process that has been 
described would just not work; but this is not a problem of 
experimental physics. 

Again, the obvious starting point for the physical interpreta- 
tion of the mathematical scheme in general relativity is the fact 
that the geometry is very nearly Euclidean in small dimensions; 
the theory approaches the classical theory in this region. There- 
fore, here the correlation between the mathematical symbols and 
the measurements and the concepts in ordinary language is un- 
ambiguous. Still, one can speak about a non-Euclidean geometry 
in large dimensions. In fact a long time before the theory of 
general relativity had even been developed the possibility of a 
non-Euclidean geometry in real space seems to have been con- 
sidered by the mathematicians, especially by Gauss in Gottingen. 
When he carried out very accurate geodetic measurements on a 



triangle formed by three mountains — the Brocken in the Harz 
Mountains, the Inselberg in Thuringia, and the Hohenhagen 
near Gottingen — he is said to have checked very carefully 
whether the sum of the three angles was actually equal to 180 
degrees; and that he considered a difference which would prove 
deviations from Euclidean geometry as being possible. Actually 
he did not find any deviations within his accuracy of measure- 

In the theory of general relativity the language by which we 
describe the general laws actually now follows the scientific 
language of the mathematicians, and for the description of the 
experiments themselves we can use the ordinary concepts, since 
Euclidean geometry is valid with sufficient accuracy in small 

The most difficult problem, however, concerning the use of 
the language arises in quantum theory. Here we have at first no 
simple guide for correlating the mathematical symbols with con- 
cepts of ordinary language; and the only thing we know from 
the start is the fact that our common concepts cannot be applied 
to the structure of the atoms. Again the obvious starting point for 
the physical interpretation of the formalism seems to be the fact 
that the mathematical scheme of quantum mechanics approaches 
that of classical mechanics in dimensions which are large 
as compared to the size of the atoms. But even this statement 
must be made with some reservations. Even in large dimensions 
there are many solutions of the quantum-theoretical equations 
to which no analogous solutions can be found in classical physics. 
In these solutions the phenomenon of the 'interference of proba- 
bilities' would show up, as was discussed in the earlier chapters; 
it does not exist in classical physics. Therefore, even in the 
limit of large dimensions the correlation between the mathe- 
matical symbols, the measurements, and the ordinary concepts is 
by no means trivial. In order to get to such an unambiguous 
correlation one must take another feature of the problem into 
account. It must be observed that the system which is treated by 
the methods of quantum mechanics is in fact a part of a much 
bigger system (eventually the whole world); it is interacting 
with this bigger system; and one must add that the microscopic 
properties of the bigger system are (at least to a large extent) 




unknown. This statement is undoubtedly a correct description 
of the actual situation. Since the system could not be the object 
of measurements and of theoretical investigations, it would in 
fact not belong to the world of phenomena if it had no inter- 
actions with such a bigger system of which the observer is a part. 
The interaction with the bigger system with its undefined micro- 
scopic properties then introduces a new statistical element into 
the description — both the quantum-theoretical and the classical 
one — of the system under consideration. In the limiting case of 
the large dimensions this statistical element destroys the effects 
of the 'interference of probabilities' in such a manner that now 
the quantum-mechanical scheme really approaches the classical 
one in the limit. Therefore, at this point the correlation between 
the mathematical symbols of quantum theory and the concepts 
of ordinary language is unambiguous, and this correlation suf- 
fices for the interpretation of the experiments. The remaining 
problems again concern the language rather than the facts, since 
it belongs to the concept 'fact' that it can be described in ordi- 
nary language. 

But the problems of language here are really serious. We wish 
to speak in some way about the structure of the atoms and not 
only about the 'facts' — the latter being, for instance, the black 
spots on a photographic plate or the water droplets in a cloud 
chamber. But we cannot speak about the atoms in ordinary 

The analysis can now be carried further in two entirely dif- 
ferent ways. We can either ask which language concerning the 
atoms has actually developed among the physicists in the thirty 
years that have elapsed since the formulation of quantum me- 
chanics. Or we can describe the attempts for defining a precise 
scientific language that corresponds to the mathematical scheme. 

In answer to the first question one may say that the concept 
of complementarity introduced by Bohr into the interpretation 
of quantum theory has encouraged the physicists to use an am- 
biguous rather than an unambiguous language, to use the clas- 
sical concepts in a somewhat vague manner in conformity with 
the principle of uncertainty, to apply alternatively different 
classical concepts which would lead to contradictions if used 
simultaneously. In this way one speaks about electronic orbits, 


about matter waves and charge density, about energy and mo- 
mentum, etc., always conscious of the fact that these concepts 
have only a very limited range of applicability. When this vague 
and unsystematic use of the language leads into difficulties, the 
physicist has to withdraw into the mathematical scheme and its 
unambiguous correlation with the experimental facts. 

This use of the language is in many ways quite satisfactory, 
since it reminds us of a similar use of the language in daily life 
or in poetry. We realize that the situation of complementarity is 
not confined to the atomic world alone; we meet it when we 
reflect about a decision and the motives for our decision or when 
we have the choice between enjoying music and analyzing its 
structure. On the other hand, when the classical concepts are 
used in this manner, they always retain a certain vagueness, they 
acquire in their relation to 'reality' only the same statistical 
significance as the concepts of classical thermodynamics in its 
statistical interpretation. Therefore, a short discussion of these 
statistical concepts of thermodynamics may be useful. 

The concept 'temperature' in classical thermodynamics 
seems to describe an objective feature of reality, an objective 
property of matter. In daily life it is quite easy to define with the 
help of a thermometer what we mean by stating that a piece of 
matter has a certain temperature. But when we try to define 
what the temperature of an atom could mean we are, even in 
classical physics, in a much more difficult position. Actually we 
cannot correlate this concept 'temperature of the atom' with a 
well-defined property of the atom but have to connect it at least 
partly with our insufficient knowledge of it. We can correlate 
the value of the temperature with certain statistical expectations 
about the properties of the atom, but it seems rather doubtful 
whether an expectation should be called objective. The concept 
'temperature of the atom' is not much better defined than the 
concept 'mixing' in the story about the boy who bought mixed 

In a similar way in quantum theory all the classical concepts 
are, when applied to the atom, just as well and just as little 
defined as the 'temperature of the atom'; they are correlated 
with statistical expectations; only in rare cases may the expecta- 
tion become the equivalent of certainty. Again, as in classical 


thermodynamics, it is difficult to call the expectation objective. 
One might perhaps call it an objective tendency or possibility, a 
'potentia' in the sense of Aristotelian philosophy. In fact, I 
believe that the language actually used by physicists when they 
speak about atomic events produces in their minds similar 
notions as the concept 'potentia'. So the physicists have grad- 
ually become accustomed to considering the electronic orbits, 
etc., not as reality but rather as a kind of 'potentia'. The 
language has already adjusted itself, at least to some extent, to 
this true situation. But it is not a precise language in which one 
could use the normal logical patterns; it is a language that pro- 
duces pictures in our mind, but together with them the notion 
that the pictures have only a vague connection with reality, that 
they represent only a tendency toward reality. 

The vagueness of this language in use among the physicists has 
therefore led to attempts to define a different precise language 
which follows definite logical patterns in complete conformity 
with the mathematical scheme of quantum theory. The result of 
these attempts by Birkhoff and Neumann and more recently by 
Weizsacker can be stated by saying that the mathematical 
scheme of quantum theory can be interpreted as an extension or 
modification of classical logic. It is especially one fundamental 
principle of classical logic which seems to require a modification. 
In classical logic it is assumed that, if a statement has any mean- 
ing at all, either the statement or the negation of the statement 
must be correct. Of 'here is a table' or 'here is not a table', 
either the first or the second statement must be correct. 'Tertium 
non datur', a third possibility does not exist. It may be that we 
do not know whether the statement or its negation is correct; 
but in 'reality' one of the two is correct. 

In quantum theory this law 'tertium non datur' is to be 
modified. Against any modification of this fundamental principle 
one can of course at once argue that the principle is assumed in 
common language and that we have to speak at least about our 
eventual modification of logic in the natural language. There- 
fore, it would be a self-contradiction to describe in natural lan- 
guage a logical scheme that does not apply to natural language. 
There, however, Weizsacker points out that one may distinguish 
various levels of language. 



One level refers to the objects — for instance, to the atoms or 
the electrons. A second level refers to statements about objects. 
A third level may refer to statements about statements about 
objects, etc. It would then be possible to have different logical 
patterns at the different levels. It is true that finally we have to 
go back to the natural language and thereby to the classical 
logical patterns. But Weizsacker suggests that classical logic 
may be in a similar manner a priori to quantum logic, as clas- 
sical physics is to quantum theory. Classical logic would then be 
contained as a kind of limiting case in quantum logic, but the 
latter would constitute the more general logical pattern. 

The possible modification of the classical logical pattern shall, 
then, first refer to the level concerning the objects. Let us con- 
sider an atom moving in a closed box which is divided by a wall 
into two equal parts. The wall may have a very small hole so 
that the atom can go through. Then the atom can, according to 
classical logic, be either in the left half of the box or in the right 
half. There is no third possibility: 'tertium non datur'. In 
quantum theory, however, we have to admit — if we use the 
words 'atom' and 'box' at all — that there are other possibilities 
which are in a strange way mixtures of the two former possibili- 
ties. This is necessary for explaining the results of our experi- 
ments. We could, for instance, observe light that has been scat- 
tered by the atom. We could perform three experiments: first 
the atom is (for instance, by closing the hole in the wall) con- 
fined to the left half of the box, and the intensity distribution of 
the scattered light is measured; then it is confined to the right 
half and again the scattered light is measured; and finally the 
atom can move freely in the whole box and again the intensity 
distribution of the scattered light is measured. If the atom would 
always be in either the left half or the right half of the box, the 
final intensity distribution should be a mixture (according to the 
fraction of time spent by the atom in each of the two parts) of 
the two former intensity distributions. But this is in general not 
true experimentally. The real intensity distribution is modified 
by the 'interference of probabilities'; this has been discussed 

In order to cope with this situation Weizsacker has introduced 
the concept 'degree of truth'. For any simple statement in an 



alternative like 'The atom is in the left (or in the right) half of 
the box' a complex number is defined as a measure for its 
'degree of truth'. If the number is i, it means that the statement 
is true; if the number is o, it means that it is false. But other 
values are possible. The absolute square of the complex number 
gives the probability for the statement's being true; the sum of 
the two probabilities referring to the two parts in the alternative 
(either 'left' or 'right' in our case) must be unity. But each 
pair of complex numbers referring to the two parts of the 
alternative represents, according to Weizsacker's definitions, a 
'statement' which is certainly true if the numbers have just 
these values; the two numbers, for instance, are sufficient for 
determining the intensity distribution of scattered light in our 
experiment. If one allows the use of the term 'statement' in this 
way one can introduce the term 'complementarity' by the fol- 
lowing definition: Each statement that is not identical with 
either of the two alternative statements — in our case with the 
statements: 'the atom is in the left half or 'the atom is in the 
right half of the box' — is called complementary to these state- 
ments. For each complementary statement the question whether 
the atom is left or right is not decided. But the term 'not de- 
cided' is by no means equivalent to the term 'not known'. 'Not 
known' would mean that the atom is 'really' left or right, only 
we do not know where it is. But 'not decided' indicates a dif- 
ferent situation, expressible only by a complementary statement. 

This general logical pattern, the details of which cannot 
be described here, corresponds precisely to the mathematical 
formalism of quantum theory. It forms the basis of a precise 
language that can be used to describe the structure of the atom. 
But the application of such a language raises a number of diffi- 
cult problems of which we shall discuss only two here: the rela- 
tion between the different 'levels' of language and the conse- 
quences for the underlying ontology. 

In classical logic the relation between the different levels of 
language is a one-to-one correspondence. The two statements, 
The atom is in the left half and 'It is true that the atom is in 
the left half,' belong logically to different levels. In classical logic 
these statements are completely equivalent, i.e., they are either 
both true or both false. It is not possible that the one is true and 



the other false. But in the logical pattern of complementarity this 
relation is more complicated. The correctness or incorrectness 
of the first statement still implies the correctness or incorrectness 
of the second statement. But the incorrectness of the second 
statement does not imply the incorrectness of the first statement. 
If the second statement is incorrect, it may be undecided whether 
the atom is in the left half; the atom need not necessarily be in 
the right half. There is still complete equivalence between the 
two levels of language with respect to the correctness of a state- 
ment, but not with respect to the incorrectness. From this con- 
nection one can understand the persistence of the classical laws 
in quantum theory: wherever a definite result can be derived 
in a given experiment by the application of the classical laws the 
result will also follow from quantum theory, and it will hold 

The final aim of Weizsacker's attempt is to apply the modified 
logical patterns also in the higher levels of language, but these 
questions cannot be discussed here. 

The other problem concerns the ontology that underlies the 
modified logical patterns. If the pair of complex numbers repre- 
sents a 'statement' in the sense just described, there should exist 
a 'state' or a 'situation' in nature in which the statement is 
correct. We will use the word 'state' in this connection. The 
'states' corresponding to complementary statements are then 
called 'coexistent states' by Weizsacker. This term 'coexistent' 
describes the situation correctly; it would in fact be difficult to 
call them 'different states', since every state contains to some 
extent also the other 'coexistent states'. This concept of 'state' 
would then form a first definition concerning the ontology of 
quantum theory. One sees at once that this use of the word 
'state', especially the term 'coexistent state', is so different 
from the usual materialistic ontology that one may doubt 
whether one is using a convenient terminology. On the other 
hand, if one considers the word 'state' as describing some po- 
tentiality rather than a reality — one may even simply replace the 
term 'state' by term 'potentiality' — then the concept of 
'coexistent potentialities' is quite plausible, since one potenti- 
ality may involve or overlap other potentialities. 

All these difficult definitions and distinctions can be avoided 




if one confines the language to the description of facts', i.e., ex- 
perimental results .However, if one wishes to speak about the 
atomic particles themselves one must either use the mathemati- 
cal scheme as the only supplement to natural language or one 
must combine it with a language that makes use of a modified 
logic or of no well-defined logic at all. In the experiments about 
atomic events we have to do with things and facts, with phe- 
nomena that are just as real as any phenomena in daily life. But 
the atoms or the elementary particles themselves are not as' real; 
they form a world of potentialities or possibilities rather than one 
of things or facts. 


The Role of Modern Physics in the 

Present Development of 

Human Thinking 


Si ■ 


THE philosophical implications of modern physics have been 
discussed in the foregoing chapters in order to show that this 
most modern part of science touches very old trends of thought 
at many points, that it approaches some of the very old problems 
from a new direction. It is probably true quite generally that in 
the history of human thinking the most fruitful developments 
frequently take place at those points where two different lines of 
thought meet. These lines may have their roots in quite different 
parts of human culture, in different times or different cultural 
environments or different religious traditions: hence if they 
actually meet, that is, if they are at least so much related to each 
other that a real interaction can take place, then one may hope 
that new and interesting developments will follow. Atomic 
physics as a part of modern science does actually penetrate in our 
time into very different cultural traditions. It is not only taught 
in Europe and the Western countries, where it belongs to the 
traditional activity in the natural sciences, but it is also studied 
in the Far East, in countries like Japan and China and India, 
with their quite different cultural background, and in Russia, 
where a new way of thinking has been established in our time; a 
new way related both to specific scientific developments of the 
Europe of the nineteenth century and to other entirely different 
traditions from Russia itself. It can certainly not be the purpose 
of the following discussion to make predictions about the prob- 
able result of the encounter between the ideas of modern physics 

1 62 


and the older traditions. But it may be possible to define the points 
from which the interaction between the different ideas may 

In considering this process of expansion of modern physics it 
would certainly not be possible to separate it from the general 
expansion of natural science, of industry and engineering, of 
medicine, etc., that is, quite generally of modern civilization in 
all parts of the world. Modern physics is just one link in a long 
chain of events that started from the work of Bacon, Galileo and 
Kepler and from the practical application of natural science in 
the seventeenth and eighteenth centuries. The connection be- 
tween natural science and technical science has from the begin- 
ning been that of mutual assistance: The progress in technical 
science, the improvement of the tools, the invention of new 
technical devices have provided the basis for more, and more 
accurate, empirical knowledge of nature; and the progress in the 
understanding of nature and finally the mathematical formula- 
tion of natural laws have opened the way to new applications of 
this knowledge in technical science. For instance, the invention 
of the telescope enabled the astronomers to measure the motion 
of the stars more accurately than before; thereby a considerable 
progress in astronomy and in mechanics was made possible. On 
the other hand, precise knowledge of the mechanical laws was 
of the greatest value for the improvement of mechanical tools, 
for the construction of engines, etc. The great expansion of this 
combination of natural and technical science started when one 
had succeeded in putting some of the forces of nature at the dis- 
posal of man. The energy stored up in coal, for instance, could 
then perform some of the work which formerly had to be done 
by man himself. The industries growing out of these new possi- 
bilities could first be considered as a natural continuation and 
expansion of the older trades; at many points the work of the 
machines still resembled the old handicraft and the work in 
the chemical factories could be considered as a continuation of 
the work in the dyehouses and the pharmacies of the older times. 
But later entirely new branches of industry developed which had 
no counterpart in the older trades; for instance, electrical engi- 
neering. The penetration of science into the more remote parts 
of nature enabled the engineers to use forces of nature which in 


former periods had scarcely been known; and the accurate 
knowledge of these forces in terms of a mathematical formula- 
tion of the laws governing them formed a solid basis for the con- 
struction of all kinds of machinery. 

The enormous success of this combination of natural and 
technical science led to a strong preponderance of those nations 
or states or communities in which this kind of human activity 
flourished, and as a natural consequence this activity had to be 
taken up even by those nations which by tradition would not 
have been inclined toward natural and technical sciences. The 
modern means of communication and of traffic finally com- 
pleted this process of expansion of technical civilization. Un- 
doubtedly the process has fundamentally changed the conditions 
of life on our earth; and whether one approves of it or not, 
whether one calls it progress or danger, one must realize that it 
has gone far beyond any control through human forces. One 
may rather consider it as a biological process on the largest scale 
whereby the structures active in the human organism encroach 
on larger parts of matter and transform it into a state suited for 
the increasing human population. 

Modern physics belongs to the most recent parts of this de- 
velopment, and its unfortunately most visible result, the inven- 
tion of nuclear weapons, has shown the essence of this develop- 
ment in the sharpest possible light. On the one hand, it has 
demonstrated most clearly that the changes brought about by 
the combination of natural and technical sciences cannot be 
looked at only from the optimistic viewpoint; it has at least 
partly justified the views of those who had always warned 
against the dangers of such radical transmutation of our natural 
conditions of life. On the other hand, it has compelled even 
those nations or individuals who tried to keep apart from these 
dangers to pay the strongest attention to the new development, 
since obviously political power in the sense o f military power 
rests upon the possession of atomic weapons. It can certainly not 
be the task of this volume to discuss extensively the political im- 
plication of nuclear physics. But at least a few words may be 
said about these problems because they always come first into the 
minds of people when atomic physics is mentioned. 

It is obvious that the invention of the new weapons, especially 


of the thermonuclear weapons, has fundamentally changed the 
political structure of the world. Not only has the concept of inde- 
pendent nations or states undergone a decisive change, since any 
nation which is not in possession of such weapons must depend 
in some way on those very few nations that do produce these 
arms in large quantity; but also the attempt of warfare on a 
large scale by means of such weapons has become practically an 
absurd kind of suicide. Hence one frequently hears the optimistic 
view that therefore war has become obsolete, that it will not 
happen again. This view, unfortunately, is a much too optimistic 
oversimplification. On the contrary, the absurdity of warfare by 
means of thermonuclear weapons may, in a first approximation, 
act as an incentive for war on a small scale. Any nation or 
political group which is convinced of its historical or moral right 
to enforce some change of the present situation will feel that the 
use of conventional arms for this purpose will not involve any 
great risks; they will assume that the other side will certainly not 
have recourse to the nuclear weapons, since the other side being 
historically and morally wrong in this issue will not take the 
chance of war on a large scale. This situation would in turn 
induce the other nations to state that in case of'small wars in- 
flicted upon them by aggressors, they would actually have re- 
course to the nuclear weapons, and thus the danger obviously 
remains. It may quite well be that in about twenty or thirty years 
from now the world will have undergone so great changes that 
the danger of warfare on a large scale, of the application of all 
technical resources for the annihilation of the opponent, will 
have greatly diminished or disappeared .But the way to this new 
state will be full of the greatest dangers. We must as in all former 
times, realize that what looks historically or morally right to the 
one side may look wrong to the other side. The continuation of 
the status quo may not always be the correct solution; it may, 
on the contrary, be most important to find peaceful means of 
adjustments to new situations, and it may in many cases be 
extremely difficult to find any just decision at all. Therefore, it is 
probably not too pessimistic to say that the great war can be 
avoided only if all the different political groups are ready to 
renounce some of their apparently most obvious rights — in view 
of the fact that the question of right or wrong may look essen- 


tially different from the other side. This is certainly not a new 
point of view; it is in fact only an application of that human 
attitude which has been taught through many centuries by some 
of the great religions. 

The invention of nuclear weapons has also raised entirely new 
problems for science and scientists. The political influence of 
science has become very much stronger than it was before World 
War II, and this fact has burdened the scientist, especially the 
atomic physicist, with a double responsibility. He can either 
take an active part in the administration of the country in con- 
nection with the importance of science for the community; then 
he will eventually have to face the responsibility for decisions of 
enormous weight which go far beyond the small circle of re- 
search and university work to which he was wont. Or he may 
voluntarily withdraw from any participation in political de- 
cisions; then he will still be responsible for wrong decisions 
which he could possibly have prevented had he not preferred the 
quiet life of the scientist. Obviously it is the duty of the scientists 
to inform their governments in detail about the unprecedented 
destruction that would follow from a war with thermonuclear 
weapons. Beyond that, scientists are frequently requested to par- 
ticipate in solemn resolution in favour of world peace; but con- 
sidering this latter demand I must confess that I have never been 
able to see any point in declarations of this kind. Such resolutions 
may seem a welcome proof of goodwill; but anyone who speaks 
in favour of peace without stating precisely the conditions ot this 
peace must at once be suspected of speaking only about that 
kind of peace in which he and his group thrive best— which ot 
course would be completely worthless. Any honest declaration 
for peace must be an enumeration of the sacrifices one is pre- 
pared to make for its preservation. But as a rule the scientists 
have no authority to make statements of this kind. 

At the same time the scientist can do his best to promote 
international co-operation in his own field. The great importance 
that many governments attach to research in nuclear physics 
nowadays and the fact that the level of scientific work is still very 
different in different countries favours international co-opera- 
tion in this work. Young scientists of many different countries 
may gather in research institutions in which a strong activity in 




the field of modern physics is going on and the common work on 
difficult scientific problems will foster mutual understanding. In 
one case, that of the Geneva organization, it has even been pos- 
sible to reach an agreement between a number of different na- 
tions for building a common laboratory and for constructing by a 
combined effort the expensive experimental equipment for re- 
search in nuclear physics. This kind of co-operation will certainly 
help to establish a common attitude toward the problems of 
science— common even beyond the purely scientific problems— 
among the younger generation of scientists. Of course one does 
not know beforehand what will grow out of the seeds that have 
been sown in this way when the scientists return into their old 
environments and again take part in their own cultural tradi- 
tions. But one can scarcely doubt that the exchange of ideas be- 
tween young scientists of different countries and between the dif- 
ferent generations in every country will help to approach with- 
out too much tension that new state of affairs in which a balance 
is reached between the older traditional forces and the inevitable 
necessities of modern life. It is especially one feature of science 
which makes it more than anything else suited for establishing 
the first strong connection between different cultural traditions. 
This is the fact that the ultimate decisions about the value of a 
special scientific work, about what is' correct or wrong in the 
work, do not depend on any human authority. It may sometimes 
take many years before one knows the solution of a problem, 
before one can distinguish between truth and error; but finally 
the questions will be decided, and the decisions are made not by 
any group of scientists but by nature itself. Therefore, scientific 
ideas spread among those who are interested in science in an 
entirely different way from the propagation of political ideas. 

While political ideas may gain a convincing influence among 
great masses of people just because they correspond or seem to 
correspond to the prevailing interests of the people, scientific 
ideas will spread only because they are true. They are objective 
and final criteria assuring the correctness of a scientific state- 

All that has here been said about international co-operation 
and exchange of ideas would of course be equally true for any 
part of modern science; it is by no means confined to atomic 


physics. In this respect modern physics is just one of the many 
branches of science, and even if its technical applications— the 
arms and the peaceful use of atomic energy— attach a special 
weight to this branch, there would be no reason for considering 
international co-operation in this field as far more important 
than in any other field. But we have now to discuss again those 
features of modern physics which are essentially different from 
the previous development of natural science, and we have for 
this purpose once more to go back to the European history of 
this development that was brought about by the combination of 
natural and technical sciences. 

It has frequently been discussed among the historians whether 
the rise of natural science after the sixteenth century was in any 
way a natural consequence of earlier trends in human thinking. 
It may be argued that certain trends in Christian philosophy led 
to a very abstract concept of God, that they put God so far 
above the world that one began to consider the world without at 
the same time also seeing God in the world. The Cartesian parti- 
tion may be called a final step in this development. Or one may 
point out that all the theological controversies of the sixteenth 
century produced a general discontent about problems that 
could not really be settled by reason and were exposed to the 
political struggles of the time; that this discontent favored 
interest in problems which were entirely separated from the 
theological disputes. Or one may simply refer to the enormous 
activity, the new spirit that had come into the European societies 
through the Renaissance. In any case during this period a new 
authority appeared which was completely independent of Chris- 
tian religion or philosophy or of the Church, the authority ot 
experience, of the empirical fact. One may trace this authority 
back into old philisophical trends, for instance, into the phi- 
losophy of Occam and Duns Scotus, but it became a vital 
force of human activity only from the sixteenth century onward 
Galileo did not only think about the mechanical motions, tne 
pendulum and the falling stone; he tried out by ™^ n ™:*}*' 
quantitatively, how these motions took Pk<^r"7fS£ 
was in its beginning certainly not meant as a deviation from the 
traditional Christian religion. On the contrary, °£^ f ^ 
kinds of revelation of God. The one was written in the Bible and 

1 68 




the other was to be found in the book of nature. The Holy Scrip- 
ture had been written by man and was therefore subject to error, 
while nature was the immediate expression of God's intentions. 

However, the emphasis on experience was connected with a 
slow and gradual change in the aspect of reality. While in the 
Middle Ages what we nowadays call the symbolic meaning of a 
thing was in some way its primary reality, the aspect of reality 
changed toward what we can perceive with our senses. What we 
can see and touch became primarily real. And this new concept 
of reality could be connected with a new activity: we can experi- 
ment and see how things really are. It was easily seen that this 
new attitude meant the departure of the human mind into an 
immense field of new possibilities, and it can be well understood 
that the Church saw in the new movement the dangers rather 
than the hopes. The famous trial of Galileo in connection with 
his views on the Copernican system marked the beginning of a 
struggle that went on for more than a century. In this contro- 
versy the representatives of natural science could argue that ex- 
perience offers an undisputable truth, that it cannot be left to 
any human authority to decide about what really happens in 
nature, and that this decision is made by nature or in this sense 
by God. The representatives of the traditional religion, on the 
other hand, could argue that by paying too much attention to 
the material world, to what we perceive with our senses, we lose 
the connection with the essential values of human life, with just 
that part of reality which is beyond the material world. These 
two arguments do not meet, and therefore the problem could 
not be settled by any kind of agreement or decision. 

In the meantime natural science proceeded to get a clearer 
and wider picture of the material world. In physics this picture 
was to be described by means of those concepts which we now- 
adays call the concepts of classical physics. The world consisted 
of things in space and time, the things consist of matter, and 
matter can produce and can be acted upon by forces. The events 
follow from the interplay between matter and forces; every event 
is the result and the cause of other events. At the same time the 
human attitude toward nature changed from a contemplative 
one to the pragmatic one. One was not so much interested in 
nature as it is; one rather asked what one could do with it. 

Therefore, natural science turned into technical science; every 
advancement of knowledge was connected with the question as 
to what practical use could be derived from it. This was true not 
only in physics; in chemistry and biology the attitude was essen- 
tially the same, and the success of the new methods in medicine 
or in agriculture contributed essentially to the propagation of the 
new tendencies. 

In this way, finally, the nineteenth century developed an 
extremely rigid frame for natural science which formed not only 
science but also the general outlook of great masses of people. 
This frame was supported by the fundamental concepts of clas- 
sical physics, space, time, matter and causality; the concept of 
reality applied to the things or events that we could perceive by 
our senses or that could be observed by means of the refined tools 
that technical science had provided. Matter was the primary 
reality The progress of science was pictured as a crusade ot 
conquest into the material world. Utility was the watchword of 

the time. . 

On the other hand, this frame was so narrow and rigid that it 
was difficult to find a place in it for many concepts of our lan- 
guage that had always belonged to its very substance, for 
instance, the concepts of mind, of the human soul or of life. 
Mind could be introduced into the general picture only as a kind 
of mirror of the material world; and when one studied the 
properties of this mirror in the science of psychology, the scien- 
tists were always tempted — if I may carry the comparison 
further— to pay more attention to its mechanical than to its 
optical properties. Even there one tried to apply the concepts of 
classical physics, primarily that of causality. In the same way lite 
was to be explained as a physical and chemical process, governed 
by natural laws, completely determined by causality. Darwin s 
concept of evolution provided ample evidence for this interpreta- 
tion It was specially difficult to find in this framework room 
for those parts of reality that had been the object of the tradi- 
ional religion and seemed now more or less only imaginary. 
Therefore in those European countries in which one was wont 
to follow the ideas up to their extreme consequences, an open 
hostility of science toward religion developed, and even in the 
other countries there was an increasing tendency toward in- 



difference toward such questions; only the ethical values of the 
Christian religion were excepted from this trend, at least for the 
time being. Confidence in the scientific method and in rational 
thinking replaced all other safeguards of the human mind. 

Coming back now to the contributions of modern physics 
one may say that the most important change brought about by 
its results consists in the dissolution of this rigid frame of con- 
cepts of the nineteenth century. Of course many attempts had 
been made before to get away from this rigid frame which 
seemed obviously too narrow for an understanding of the essen- 
tial parts of reality. But it had not been possible to see what 
could be wrong with the fundamental concepts like matter 
space, time and causality that had been so extremely successful 
in the history of science. Only experimental research itself, car- 
ried out with all the refined equipment that technical science 
could offer, and its mathematical interpretation, provided the 
basis for a critical analysis— or, one may say, enforced the critical 
analysis— of these concepts, and finally resulted in the dissolu- 
tion of the rigid frame. 

This dissolution took place in two distinct stages. The first 
was the discovery, through the theory of relativity, that even 
such fundamental concepts as space and time could be changed 
and in fact must be changed on account of new experience. This 
change did not concern the somewhat vague concepts of space 
and time in natural language; but it did concern their precise 
formulation in the scientific language of Newtonian mechanics 
which had erroneously been accepted as final. The second stage 
was the discussion of the concept of matter enforced by the ex- 
perimental results concerning the atomic structure. The idea of 
the reality of matter had probably been the strongest part in that 
rigid frame of concepts of the nineteenth century, and this idea 
had at least to be modified in connection with the new ex- 
perience. Again the concepts so far as they belonged to the 
natural language remained untouched. There was no difficulty 
in speaking about matter or about facts or about reality when 
one had to describe the atomic experiments and their results. But 
the scientific extrapolation of these concepts into the smallest 
parts of matter could not be done in the simple way suggested 
by classical physics, though it had erroneously determined the 



general outlook on the problem of matter. 

These new results had first of all to be considered as a serious 
warning against the somewhat forced application of scientific 
concepts in domains where they did not belong. The application 
of the concepts of classical physics, e.g., in chemistry, had been 
a mistake. Therefore, one will nowadays be less inclined to 
assume that the concepts of physics, even those of quantum 
theory, can certainly be applied everywhere in biology or other 
sciences. We will, on the contrary, try to keep the doors open 
for the entrance of new concepts even in those parts of science 
where the older concepts have been very useful for the under- 
standing of the phenomena. Especially at those points where the 
application of the older concepts seems somewhat forced or 
appears not quite adequate to the problem we will try to avoid 
any rash conclusions. 

Furthermore, one of the most important features of the de- 
velopment and the analysis of modern physics is the experience 
that the concepts of natural language, vaguely defined as they 
are, seem to be more stable in the expansion of knowledge than 
the precise terms of scientific language, derived as an idealization 
from only limited groups of phenomena. This is in fact not sur- 
prising since the concepts of natural language are formed by the 
immediate connection with reality; they represent reality. It is 
true that they are not very well defined and may therefore also 
undergo changes in the course of the centuries, just as reality 
itself did, but they never lose the immediate connection with 
reality. On the other hand, the scientific concepts are idealiza- 
tions; they are derived from experience obtained by refined 
experimental tools, and are precisely defined through axioms 
and definitions. Only through these precise definitions is it pos- 
sible to connect the concepts with a mathematical scheme and to 
derive mathematically the infinite variety of possible phenomena 
in this field. But through this process of idealization and precise 
definition the immediate connection with reality is lost. The con- 
cepts still correspond very closely to reality in that part of nature 
which had been the object of the research. But the correspond- 
ence may be lost in other parts containing other groups of 

Keeping in mind the intrinsic stability of the concepts of 

I 7 2 



natural language in the process of scientific development, one 
sees that— after the experience of modern physics— our attitude 
toward concepts like mind or the human soul or life or God will 
be different from that of the nineteenth century, because these 
concepts belong to the natural language and have therefore 
immediate connection with reality. It is true that we will also 
realize that these concepts are not well defined in the scientific 
sense and that their application may lead to various contradic- 
tions, for the time being we may have to take the concepts 
unanalyzed as they are; but still we know that they touch reality! 
It may be useful in this connection to remember that even in the 
most precise part of science, in mathematics, we cannot avoid 
using concepts that involve contradictions. For instance it is 
well known that the concept of infinity leads to contradictions 
that have been analyzed, but it would be practically impossible 
to construct the main parts of mathematics without this concept. 
The general trend of human thinking in the nineteenth cen- 
tury had been toward an increasing confidence in the scientific 
method and in precise rational terms, and had led to a general 
scepticism with regard to those concepts of natural language 
which do not fit into the closed frame of scientific thought-for 
instance, those of religion. Modern physics has in many ways in- 
creased this skepticism; but it has at the same time turned it 
against the overestimation of precise scientific concepts, against 
scepticism itself. The scepticism against precise scientific con- 
cepts does not mean that there should be a definite limitation for 
the application of rational thinking. On the contrary, one may 
say that the human ability to understand may be in a certain 
sense unlimited. But the existing scientific concepts cover always 
only a very limited part of reality, and the other part that has 
not yet been understood is infinite. Whenever we proceed from 
the known into the unknown we may hope to understand but 
we may have to learn at the same time a new meaning of the 
word 'understanding'. We know that any understanding must 
be based finally upon the natural language because it is only 
there that we can be certain to touch reality, and hence we must 
be sceptical about any scepticism with regard to this natural 
language and its essential concepts. Therefore, we may use these 
concepts as they have been used at all times. In this way modern 


physics has perhaps opened the door to a wider outlook on the 
relation between the human mind and reality. 

This modern science, then, penetrates in our time into other 
parts of the world where the cultural tradition has been entirely 
different from the European civilization. There the impact of 
this new activity in natural and technical science must make 
itself felt even more strongly than in Europe, since changes in 
the conditions of life that have taken two or three centuries in 
Europe will take place there within a few decades. One should 
expect that in many places this new activity must appear as a 
decline of the older culture, as a ruthless and barbarian attitude, 
that upsets the sensitive balance on which all human happiness 
rests. Such consequences cannot be avoided; they must be taken 
as one aspect of our time. But even there the openness of modern 
physics may help to some extent to reconcile the older traditions 
with the new trends of thought. For instance, the great scientific 
contribution in theoretical physics that has come from Japan 
since the last war may be an indication for a certain relationship 
between philosophical ideas in the tradition of the Far East and 
the philosophical substance of quantum theory. It may be easier 
to adapt oneself to the quantum-theoretical concept of reality 
when one has not gone through the naive materialistic way of 
thinking that still prevailed in Europe in the first decades of this 

Of course such remarks should not be misunderstood as an 
underestimation of the damage that may be done or has been 
done to old cultural traditions by the impact of technical prog- 
ress. But since this whole development has for a long time passed 
far beyond any control by human forces, we have to accept it as 
one of the most essential features of our time and must try to 
connect it as much as possible with the human values that have 
been the aim of the older cultural and religious traditions. It may 
be allowed at this point to quote a story from the Hasidic re- 
ligion: There was an old rabbi, a priest famous for his wisdom, 
to whom all people came for advice. A man visited him in 
despair over all the changes that went on around him, deploring 
all the harm done by so-called technical progress. 'Isn't all this 
technical nuisance completely worthless,' he exclaimed, 'if one 
considers the real values of life?' 'This may be so,' the rabbi 




replied, 'but if one has the right attitude one can learn from 
everything.' 'No,' the visitor rejoined, 'from such foolish things 
as railway or telephone or telegraph one can learn nothing 
whatsoever.' But the rabbi answered, 'You are wrong. From 
the railway you can learn that you may by being one instant late 
miss everything. From the telegraph you can learn that every 
word counts. And from the telephone you can learn that what 
we say here can be heard there.' The visitor understood what the 
rabbi meant and went away. 

Finally, modern science penetrates into those large areas of 
our present world in which new doctrines were established only 
a few decades ago as foundations for new and powerful societies. 
There modern science is confronted both with the content of the 
doctrines, which go back to European philosophical ideas of the 
nineteenth century (Hegel and Marx), and with the phe- 
nomenon of uncompromising belief. Since modern physics must 
play a great role in these countries because of its practical ap- 
plicability, it can scarcely be avoided that the narrowness of the 
doctrines is felt by those who have really understood modern 
physics and its philosophical meaning. Therefore, at this point 
an interaction between science and the general trend of thought 
may take place. Of course the influence of science should not be 
overrated; but it might be that the openness of modern science 
could make it easier even for larger groups of people to see that 
the doctrines are possibly not so important for the society as had 
been assumed before. In this way the influence of modern 
science may favour an attitude of tolerance and thereby may 
prove valuable. 

On the other hand, the phenomenon of uncompromising belief 
carries much more weight than some special philosophical no- 
tions of the nineteenth century. We cannot close our eyes to the 
fact that the great majority of the people can scarcely have any 
well-founded judgment concerning the correctness of certain 
important general ideas or doctrines. Therefore, the word 
'belief can for this majority not mean 'perceiving the truth of 
something' but can only be understood as 'taking this as the 
basis for life'. One can easily understand that this second kind 
of belief is much firmer, is much more fixed than the first one. 
that it can persist even against immediate contradicting ex- 


perience and can therefore not be shaken by added scientific 
knowledge. The history of the past two decades has shown by 
many examples that this second kind of belief can sometimes be 
upheld to a point where it seems completely absurd, and that it 
then ends only with the death of the believer. Science and history 
can teach us that this kind of belief may become a great danger 
for those who share it. But such knowledge is of no avail, since 
one cannot see how it could be avoided, and therefore such belief 
has always belonged to the great forces in human history. From 
the scientific tradition of the nineteenth century one would of 
course be inclined to hope that all belief should be based on a 
rational analysis of every argument, on careful deliberation; and 
that this other kind of belief, in which some real or apparent 
truth is simply taken as the basis for life, should not exist. It is 
true that cautious deliberation based on purely rational argu- 
ments can save us from many errors and dangers, since it allows 
readjustment to new situations, and this may be a necessary 
condition for life. But remembering our experience in modern 
physics it is easy to see that there must always be a fundamental 
complementarity between deliberation and decision. In the prac- 
tical decisions of life it will scarcely ever be possible to go 
through all the arguments in favour of or against one possible 
decision, and one will therefore always have to act on insufficient 
evidence. The decision finally takes place by pushing away all 
the arguments — both those that have been understood and 
others that might come up through further deliberation — and 
by cutting off all further pondering. The decision may be the 
result of deliberation, but it is at the same time complementary 
to deliberation; it excludes deliberation. Even the most important 
decisions in life must always contain this inevitable element of 
irrationality. The decision itself is necessary, since there must 
be something to rely upon, some principle to guide our actions. 
Without such a firm stand our own actions would lose all force. 
Therefore, it cannot be avoided that some real or apparent truth 
form the the basis of life; and this fact should be acknowledged 
with regard to those groups of people whose basis is different 
from our own. 

Coming now to a conclusion from all that has been said about 
modern science, one may perhaps state that modern physics is 



just one, but a very characteristic, part of a general historical 
process that tends toward a unification and a widening of our 
present world. This process would in itself lead to a diminution 
of those cultural and political tensions that create the great 
danger of our time. But it is accompanied by another process 
which acts in the opposite direction. The fact that great masses 
of people become conscious of this process of unification leads to 
an instigation of all forces in the existing cultural communities 
that try to ensure for their traditional values the largest possible 
role in the final state of unification. Thereby the tensions increase 
and the two competing processes are so closely linked with each 
other that every intensification of the unifying process— for in- 
stance, by means of new technical progress— intensifies also the 
struggle for influence in the final state, and thereby adds to the 
instability of the transient state. Modern physics plays perhaps 
only a small role in this dangerous process of unification. But it 
helps at two very decisive points to guide the development into 
a calmer kind of evolution. First, it shows that the use of arms 
in the process would be disastrous and, second, through its open- 
ness for all kinds of concepts it raises the hope that in the final 
state of unification many different cultural traditions may live 
together and may combine different human endeavours into a f 
new kind of balance between thought and deed, between activity 
and meditation.